During a recent police visit, we were standing in the living room and I was asked by one of the officers if they could have a look around.  The bedroom door was closed (as it's next to the front door I want a bit of privacy) and I said no.  The officer kept on asking and made comments like 'what is the problem', and I still said no.  Eventually I gave in as I felt they weren't going to leave unless I agreed.

Can they do this?

Well, my understanding (admittedly from watching police shows on TV) is that once you've invited them in, they can have a look round. At least they asked, rather than pretending to use the bathroom then sneaking around without you knowing. If their visit was for the obvious reason, then you'll need to get used to being under suspicion all the time and having very little privacy, unfortunately.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

Up till this point I've never had any problems with the local officers and to be honest I've actually found a lot of their visits to be useful and non-intrusive.  I've always been honest with them and found them easy to talk to, in fact the current officer I deal with has said that I can ramble on at times.

I know the reason why they asked, but it was the way that they repeatedly asked and didn't want to take no as an answer that makes me think they needed my permission.

As I said, my information comes from watching too much TV, so I may well be wrong. Having said that, I've just found this online, and it looks like there is a difference between inviting them in and letting them search. You have to let them in, sooner or later, so you didn't invite them in, but that doesn't automatically give them the right to search, which is why they asked. If you kept saying no, they would just keep asking and I daresay it wouldn't look good on your risk assessment.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

I find the questions they ask 100% more intrusive than them having a poke around my stuff. As AB said, your privacy pretty much goes out of the window.
If you think that they cross the line at all, however, don't be afraid to ring Unlock or get some advice from your legal person. I've done this and pushed back on a couple of things since.

I'm sure you wouldn't ... but... if you have anything you even remotely don't want them to stumble on while nosing around, just get rid. For your own peace of mind if nothing else.

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Fighting or Accepting - its difficult to know which is right and when.

Does a Britney Spears album come under that heading? :-/

There is nothing illegal about a Britney Spears album (except the quality of her singing could be classed as criminal in some respects... joking). Is it a signed copy, or collector's item? Then absolutely keep it.

But if you're worried about something like that, it comes back to what I said about peace of mind, is it worth keeping if you're going to worry about it? It's easy to listen to music online these days too.

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Fighting or Accepting - its difficult to know which is right and when.

I assume that is a sarcastic comment and not a serious question????

Probably better than having a Michael Jackson album lying around!

One's paranoia is heightened once you're thrown into a world you're not familiar with, especially when your every move is now questioned.
I don't think the mental health of those in that position is taken into account at all and god forbid anyone showing sympathy to an offender because they "brought it on themselves".
Everyone's all for dropping the hammer but nobody cares about the aftermath.

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Fighting or Accepting - its difficult to know which is right and when.

The police illegally searched my home and car (took lots for 'analysis' but found nothing). Nobody gives two hoots. I suppose depending on your conviction you could take legal action of go to the papers, but that will just dredge up what you have supposedly done. They know you are unlikely to do anything...