Not many summer schools specialise in young kids, but if they do I'm fairly sure they'd employ an experienced primary school teacher. Although it's a little early for summer school job ads, you should easily be able to find the details of a few online and contact them to ask.
If you want to teach EFL longer term, want to teach abroad, want to teach teens or adults or want a larger range of schools to apply for, you will need something like CELTA (which is a qualification, the organisation is Cambridge ESOL). In fact, I'd recommend it anyway as I've seen plenty of primary school teachers struggle to adapt to the very different kind of teaching needed in TEFL.
Finally, although teaching adults English is probably easier than primary school teaching (at least in some ways), I wouldn't say the same for summer schools for small kids. You'll have one day off a week and be expected to be on call at literally any other time, with kids whose languages and probably cultures you know nothing about. For that, you'll probably get a contract that pays around the national minimum wage and quite possibly breaks EU employment law.