Seeing that it's an automated registration program, then you are able to put through the domain name registration in a made up company name.
However, problems may arise if you ever need to prove to Nominet that you own the domain, e.g. you want to transfer the domain name to someone else. When you do this, they normally require proof that you are the individual who currently owns the domain name.
If you're not going to transfer the domain, then it is unlikely that anything will ever come of registering in a made up company name, seeing that the renewal process is automatic. However, others here may have different opinions.
Note, I have checked with Nominet that you don't have to give your full name when registering, e.g. if you're called Mark Simon Harris, then registering as M. Harris is accepted, although they may need more proof of ID when transferring the domain.
If you have a common surname, then registering as something like M. Harris is effectively anonymous anyway, because there will be so many of them out there. I guess it also slightly increases your chances of a fradulent domain transfer away from you, because someone else could pretend to be you more easily. However, Nominet will normally ask for proof of address too.
Finally, there are ID protect services that you can pay for.
www.enom.com offer this service, but it makes your whole registration more expensive when compared to a company like
123reg.co.uk.
I'd be interested to hear other people's thoughts on cost effective and legal ways to keep your registration anonymous.
HTH
All the best
accelerator