So having emailed the ICO to seek further clarification onthe matter I received a reply which stated

“More prominent – or more meaningful results - tend to be returned in the first six pages of a search on an individual’s name using the Google search facility. Searching for results can be time-consuming and wetherefore generally limit searches to six or seven pages of results. These areinternal guidelines. To my knowledge, not all our guidelines are included inour published casework process.”

My mind boggles… So now its six or seven pages of results. It seems as though this guideline changes whenever its suits ! I just find this truly shocking behaviour. Utter shameful.

Sounds like potentially these internal guidelines don't exist or aren't official if the definition isn't set in stone and is changing.  If it were me I'd be asking for the section within the GDPR regulations that specifically state erasure is only limited to the first 'six or seven pages' of data and all other data can be retained by the data controller regardless.  I'd also be asking for a copy of the internal guidelines and if (when) they don't provide these I'd be asking (them) how I make a FOI request to obtain said guidelines.

I'd also try to bring those links to within their guidelines of six or seven pages - not by trying to get them to move up the ranks but trying to search for them from different locations or adding keywords such as the town/city or street name etc (something relevant to a search someone would do that brings higher up the pages). Although it would be an interesting exercise to see if you could bring them up the ranks enough to met their criteria and then see how they handle the request.

Hmmm, if the case worker considers it too "time consuming" to click to page 6 or 7 to simply confirm the results appear, then it doesn't give me much faith that she/he will actually do the work necessary to determine whether or not you're results should be delisted. It would have taken less amount of time to do the search than write the email. So I don't think this case worker is acting in good faith. "page 6 or 7" is a fairly vague guideline, when do they decide whether or not they click on page 7, and again "generally limit" - when do they divert from the "generally"? Of course the reality is the ranking of search results changes, so a result on page 6 today, could be on page 4 tomorrow. Indeed if you were successful in getting the higher ranking results delisted, then it is likely that the lower ranking results would just move up the ranking. Obviously the fact you and others are aware that Google is ranking these results means it is prominent, and the word "meaningful" is rather strange. Surely, the reason you are trying to delist them is because you don't think the results are meaningful, and paint an unfair picture of yourself.
You need to make the job easy for this caseworker, send a list of all the URLs, with screendumps of them circled. That will be all the evidence they should need to know they exist, they shouldn't even need to do the search themself then. I would probably spend some time for each result listing the arguments in favour of delisting.
If this is a true guideline and one of the purposes is to save time, it would be logical to have that published online, that would discourage people from contacting them. You could go down the twitter route if you want to shame them: https://twitter.com/iconews?lang=en
An FOI request might be a good idea, I would certainly like to see their guidelines. It is likely to annoy them.

I haven't read all of this thread, so apologies if this has already been covered, but I'm stunned by how clueless the ICO are and would like to add my own experience: 

Several years ago I applied for results related to my name to be delisted (a link to a newspaper article about an old conviction). The article appeared on page 1 when I searched for my name AND my current employer, but the ICO refused my request because when they searched for it, they couldn't see the result anywhere. Clearly, they have no idea how a search engine works. The search results will vary significantly depending on a wide range of factors: previous search history, browser, location and time of day amongst others. These are variables in every search algorithm. 

My point is: which page a listing appears on in a search shouldn't be a factor in the ICO's decision making process. This is because for some people it will appear on page 1 (maybe because their IP address is local to the newspaper in question), but for others it could be on page 1,000 (because they are searching from the other end of the country). All that matters is if it is listed in major search engines. If anything, it would the ICO's job easier by streamlining the process and making it a more universal rule.

At the moment, as an organisation the ICO are really not fit for purpose. I'll end with one last example to demonstrate this. When I first made my application (this was several years back) it took them several months and several reminder emails to get back to me. They declined the application on the grounds that I didn't supply the required information. They didn't tell me any more than that. For some reason, they returned my original documentation in an email and when I checked this, I noticed that the PDF form had cut off a huge chunk of the information I had supplied. I checked the original document I had sent them which didn't have this issue - so somewhere, at some point, they messed something up in the formatting and just decided to dismiss the application (after months of waiting). They didn't even let me send them the original form, and told me I had to start the application from scratch.

Apologies for the long rant, but it's helpful to know what we're working with here!     

Thank you for your comments I appreciate it. So I’m going to take a few days to think this over before I take my next steps however I don’t feel i can just leave it be and feel the need to ensure others don’t come across this issue. It has to be resolved one way or another and as most solicitors firms are only interested in the pay packet and don’t really care too much about peoples lives it would seem action is required. I do not know how far I will get but I think I owe it to myself and anyone else who is being fobbed off. My guts instinct tells me that although an independent organisation I feel they themselves are stereotyping people and pre judging individuals, I feel they like so many are scared to act and remove things just in case that person goes on to do something bad and the information about a de-listing to come out.

I think my first step will be to speak to a few solicitorfirms to ask what sort of push back they have gotten in relation to this “6 or7” page nonsense. Once I have got an idea from them hopefully this will shed some light and give me a little more understanding but currently, I feel something is not right here and needs exploring.

The funny thing about the whole case is that I don’t / didn’texpect the ICO to agree with me however I did expect a more professional approachand at the very least for them to consider the evidence I provided having spendseveral weeks to produce the 9 page document including case law, judgements, amongst other things. The 1 URL (BBC) that they have provided reasons for not taking action against I fully understand the reasoning so its not as though i am being unreasonable. I just want the other 5 URL's to be looked at and a judgement made and not simply we wont look at them because its outside our guidelines of 6 or 7 pages.