I have overstayed my holiday visa in the U.S and want to go home to England; how do I go about doing so?
Can the British embassy help me get home to the UK?
You can just buy a ticket home and leave the USA. No need for help with that.
But you will not easily be able to get back into the USA. Almost everybody who overstayed can not use the 'no visa' option anymore and it will become much harder to get a normal visitors visa. Your embassy can also not help you there, you broke the rules, you suffer.
As mentioned by @phoog in the comments:
I would note here that you should be aware of the automatic 3- or 10-year ban that may be triggered when you leave the US. If you accrue more than 180 days of illegal presence, you get a 3 year ban from the day you leave the US. If you accrue more than a year of illegal presence, the ban is 10 years. If you think you'll want to return to the US, you should leave before day 180 if at all possible. But because your future credibility as a visitor is worse the longer you stay, you should leave as soon as you can.
Answering the specific question, no, it can't. From the government's webpage on the subject:
Pay any bills or give you money because we are not funded to do this and you would not get these bills paid for you if you were in the UK. You should take responsibility for yourself. It would be unfair for those who take out insurance to subsidise those who do not
Make travel arrangements for you ... because these are private arrangements which are your responsibility to make for yourself