johnnyk,
You shouldn't lose any time on extensions so in your example of applying on day 45 of the 60 day entry stamp, your 30 days will start from the 60th day. I've done extensions to tourist visas plenty of times in the past and have never lost a day.
However, if you exited and re-entered Thailand to activate the second entry early then you would lose the time on coming back in.
To the OP, a couple of things. Firstly make absolutely sure that when you re-enter to get your second 60 days, that the visa is still valid. If it's expired you'll only get 15 days at a land or sea border or 30 days at the airport. That's why chopsticks and I have impressed on you not to get the visa a long time in advance.
Secondly, some Embassies are getting tough with giving double entries and although I should think you'll be OK in London, you might want to also consider applying from Hull. Postal applications are accepted there whereas personal presence is required at The Embassy both for application and collection. The only additional cost to Hull will be that of registered mail there and back -
http://www.thaiconsul-uk.com/ If you go to The Embassy, I'd call them first to make sure they'll issue a double-entry visa unless other members have recent experience of this situation and been successful.