True, there is no "magic number" over here like the standard Fair Isaac credit score used in the US. If you request credit over here, the institute you request it from will asses your circumstances, and probably give you their own (non-public) credit score. So, for example, simply because you are approved for a credit card by one bank, does not mean you'll be approved for a similar one from another bank. Different banks have different levels of risk they are willing to accept by taking on a customer.
Equifax and Experian are the two main credit reference agencies in the UK, and they both offer a service where they will tell you your "credit score", this is basically a number similar to the US credit score, and is a good indication of how credit worthy you are. This doesn't necessarily mean you will get credit if this score is good, as I said, different banks interpret the data in different ways, and what is a credit plus in one bank's opinion may be a negative in another's opinion.
Identity matching, also, is more difficult in the UK, as we do not base everything on national insurance/social security number. There is a very good reason for this, the Data Protection Act. I suspect a lot of Americans would be surprised at the volume of information the private sector holds on them, all through their social security number. Thankfully, despite all the press reports that we're a Big Brother state, that sort of tracking of information is forbidden in the UK unless you expressly give your permission for it.
