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?
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.
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.