Hard to say without seeing your code and knowing the tech you work with, but I'd assume a lot more than £20k. Is that one and a half years of coding, or one and a half years since graduating?
I graduated a year and a half ago and have been with my current company since then. I used to work part time as a developer during university so I've probably got closer to two years worth of software engineering in a business environment.
Whilst I would say that a lot of my day to day stuff is what most would consider bog-standard standard web development, we do get to dabble in dealing with big data, being our own sysadmins and bringing our software to other platforms i.e. there is a lot of emphasis put on learning where I currently am and researching and incorporating new technologies is always encouraged.
You might be better off not gauging yourself by what others earn (or claim to earn..), but by looking at where you'd want to live in London, how much you're willing to travel, do you still want a car, etc.
Call some estate agents or get on rightmove and look for 1 bedroom apartments near the new office location. If it's going to cost £10k per year more than the equivalent where you currently live (not your current home of course, pick somewhere nicer, it's a negotiation...), then that's a decent starting place for discussions.
London is a seriously expensive place, earning £20-£25k a year there is going to be no fun, I think you should be looking at £30k plus, and if they don't want to pay you it, then fair enough, but I probably wouldn't want to live there.
When you consider that a newly qualified teacher working in inner-city London is paid £6k a year more than the same qualified teacher elsewhere in the UK (£27k inner-city London) http://www.tda.gov.uk/get-into-teaching/salary/pay-and-benef... , then that should give you a decent idea of what you're going to want to get paid over and above your current salary.
