If he registers as unemployed (and indicates that he's seeking a temporary job, of any kind, until he starts his full-time employment) he'll be eligible for Job-Seekers' Allowance (or whatever it's called under the the new unified arrangements). If he's made sufficient NI contributions he'll get contribution-based JSA, which isn't means tested. If not he can be considered for income-based JSA, which is means-tested. (He has to fill in the same form in either case, which requires him to declare his savings and any income he might be in receipt of. He'll also have to attend an interview).
If he's got any holiday planned though he'll have to sign off JSA for the relevant period and then sign on again when he returns. (Anyone leaving the country, even if only to nip across to Dover for a few hours to buy some cheap booze) is required to sign off JSA and then go through the whole signing-on process again, including the interview, upon their return).
He should also be eligible for Housing Benefit, which is available to anyone on a low income (irrespective of whether they're working or not):
https://www.gov.uk/housing-benefit/overview
Claiming benefits all comes down to a lot of form filling (and submitting documents, such as the past 6 month's bank statements) and can be tedious in the extreme but it'll be worth it in the end.
He might not have to wait until the end of the month for his first salary payment though. Many teachers are paid in the middle of the month that they're working. (When I started teaching, the school term didn't start until a week into September. I got my first month's pay only just over a week later!)