Are you between 18 and 20. If you are 21 or over. 7.50 is legally way to low. But almost exactly minimum wage for 18 to 20. Do not accept below due to no contract. It makes no difference.
Record everything. Even if its self written notes about hour conversations and promises. Ensure you have some form of time sheet. Even if you write your own and give him a copy.
No contract is likely a way to evade paying the employer share of NI and avoid paying your share of taxes. Technically you would be working as a sole trader. So technically would have to pay it yourself. If he tells you your a sole trader/contractor. He is avoiding his NI not evading. Ie legally. But it means you pay more. Assuming you follow the rules.
Not to complex if you decide to do it. Gov sites give lots of guidance. But you want much more then min wage.
Odds are high. He is actually in the same situation and working under the table.