Postdoc salary negotiation (UK)
This depends heavily on the funding source. For all UK funded postdocs the pay will be set on the national scale - current rates without London weighting are up-to-date, but I'm not sure if the comments about the London weighting are correct.
For research council funded postdocs I would expect the salary range to be fixed somewhere between spine point 27 and 40, with the initial upper limit more likely around spine point 34. This is close to the numbers you quote. I would not expect much flexibility unless they can find additional funds to supplement the (fixed) funding from the grant.
On the salary increase in post: there would typically be a 1 (one!) spine point increment after the second year. I'd be very surprised if a substantial increase along the lines you're wanting could be negotiated, let alone after the first year.
If the funding is not pure research council then there may be more flexibility.
As someone who's been on both sides: I have fielded salary questions, particularly from overseas candidates, and (done sensitively) I don't think it will be held against you. The above is more a warning that the constraints of RCUK funding may make it impossible to get a solution that's acceptable to you.
You have the same issue that many people do.
The cost of living in London (rent or buying a home) is often double what it is outside of London, yet salaries are about the same in London as elsewhere in the UK.
It is common for professionals (e.g. computer programmers) in their 30s to not be able to afford more than a small room in a shared house if they choose to live in London. Expecting to support a family on any “normal” single salary in London is unreasonable.
If you are willing to spend 2hr each way commuting, then you can get a lot cheaper housing, but your train ticket will often be over £5K a year. But why have a family if you are commuting so much…?
When I was searching for a post-doc position, during the phone interview with the PI asked about salary. I just told him I have a family. He said he could get me something a little higher than what they were advertising. Basically, in academia, a good PI will understand your situation because he's been there.
Expanding on Ian's excellent answer, there is a best practice for salary negotiation. Your instinct is correct: don't mention money in a cover letter. They will ask you about money at some point. You are not wasting anyone's time if you are applying for a job you are seriously interested in taking. They expect to interview many candidates and have some offers they make rejected. And you should not expect that both parties could understand the complete situation from your cover letter.
The correct response to the money question for a post-doc position is simply to state you have a family to support and you'd like them to do the best they can for you. As Ian pointed out there may only be so much they can do.
Once you get an offer, you can decide if that's enough. If it's not, you can always call and tell them you'd sign instantly if you could get +x instead, if indeed that's the case. It may be they cannot. However, once they are trying to get you (i.e. post-offer), you chances are maximized.