Brighton - summer job: Where to live?

You would need to seek accommodation fairly remote from the sea front, in order for it to be cheap and to be able to park a car at no expense. Your employment would probably be near the seafront so you would have to walk to it or take the bus - no chance of parking near the seafront except at vast expense.

Look for bedsits in Brighton then what do you expect us to do

That is the least of your worries. Come the end of March we will no longer be in the EU so you might have to get a work visa.

Don't worry about the car. Brighton has an excellent public transport system with frequent fast trains to Gatwick Airport (25 minutes) and London Victoria (57 minutes). Parking is difficult. Google 'Bedsits for rent Brighton'. Depending on which country you are from and the progress of negotiations with the EU you may need a visa

First get the job, THEN worry about the washing machine.

I'm not from Brighton but I am aware it is not a cheap town to live in, especially with your list of living requirements.

In reality the landlord could rent out such accommodation as a holiday let for probably 4 times during high season for what the residential rental rate to would be.