OP - I would make sure he sees a GP and also push for epipens. I know they are serious to use but as someone with very severe anaphylaxis and who is outdoorsy epipens have been the difference of life and death whilst waiting for help to come.
Make sure he's (and then you) is properly trained in how to use them as there is a knack (it's easy but there's a few things he should know).
@FictionalCharacter it depends on what you mean by mild reactions, but no GP is going to mind you going to discuss this with them. Most are very clued up on anaphylaxis in my experience and will fight to get screening done if needed (most can actually do a basic screening in the surgery).
There's some really awful advice on this thread regarding the seriousness of reactions - mouth swelling is classed as serious.
Reminder for all
Epipens should always be carried in pairs, in case one fails or is wrongly administered.
You can have individual plans for it - so for me planes require four epipens to come with me, we have two in the house, and then two in the car, and two on me, plus two at relatives we stay at often.
Check them regularly to make sure they are in date - they expire quite frequently and this is the biggest cause of failure.
Each brand works in a slightly different way, and there's two doses of pens, so make sure the pharmacist has given you the correct dose as per prescription.
You can get training pens to show people close to you how to use them - these absolutely must be kept in a completely different place from non-training pens though.
Predisolone is usually advised to be administered at the same time (along with other antihistamins depending on case/severity).
Epi pens can be administered by other people - they are exempt from the medication law that medications cannot be administered by anyone other than the person. This is a really common myth particularly in work places / with HR. They are absolutely exempt and no one should hesitate to use one if needed.