Lots to consider here I guess.
You live really near to LHR, so a short commute is indeed invaluable! I personnally rate it very highly in my life and wouldn't change it for more cash (I live 10mins away from work).
BMED is indeed a franchise and to be honest have heard mixed reviews. We have people working at LGW who used to work for BMED, so it might be worth searching them out and having a word with them. I thought does occur to me though that why are they at LGW fo BMED was so good?
BMED from what I know is all trips so if guaranteed time away is what you want, then it might be the right option.
At LGW because you are brand new there is no way you can guarentee trips (especially long haul ones), so if a totally trip orientated roster is what your looking for, expect disappointment. I would add to though that many people have been working for EFLGW for years as Main Crew and made a living out of it.
I would also add that you need to decide if flying is going to be career. It if is, then I would say stay at LGW because the career paths are only limited to where you want to go. You can move on to PSR and then to CM if you want to stay flying. If you bide your time you can transfer to LHR. Or you can go into other areas such as a job at Cranebank or Waterside. At BMED the choices are far more limited.
It all depends on what YOU want.
What do you NEED to earn every month? Money is not the be all and end all of everything. Obviously it helps. But a job that you wake up and enjoy coming to every morning is in my opinion far more important. It's a large part of your life, so make sure you like it.
I would urge you to search out more information on BMED before making a decision. Talk to people who work for them and compare what they say to your current working condidtions. Also remember SFLGW is still not fully up and running until Feb, so an accurate picture of how things will be will not able to be formed until March at least.
Be aware that any advice you do get from anyone will not always be impartial depending on where they work ( I have tried to be impartial here, however I am not a BMED expert so can't comment too much on them).
Good luck anyway what ever you decide.