I’ve been using the same cheap wireless charger I got from Amazon for my iPhone X, iPhone XR and now my iPhone 11. No problems with any of them. XR was still at 100% battery health when sold after 10 months.
So £800 phone and using £5 charger does seem a little off.
I bought a 3rd party charger on Apple Store that the electronics were terrible, £45. Now I stick to Samsung - two, one flat, one upright, and known brands, and take into account cable + outlets, and preferably on UPS surge.
Only thing that could go wrong is the wireless charger is less efficient and generates more heat while charging plus charges the phone slower for this reason.
This could result in premature battery degradation, but you most certainly notice this problem before any harm is done anyway.
There’s quite a few wireless chargers out there, some have different types of build quality, but if you can purchased one, try to find a reputable brand as someone else mention like ‘Anker’. Not also have they been in the battery business for years, but they partnered with some other companies that share their same values and goals with craftsmanship/customer service.
My son managed to damage the charging cable. He pushed something against the charger, the cable was bent back and something shorted inside.
It was charging his ipad at the time and damaged the charge circuit so that it would only charge when switched off. When up and running, it would show it was charging but in reality wasn't.
So, from that lesson I would say yes. If you have a problem with the charger and it shorts inside because it's badly manufactured, then it can definitely damage your phone.
And naturally, it could electrocute someone or set fire to your house.
These things are often left plugged in for very long periods of time and forgotten about, so plenty of time to overheat.
I wouldn't go so far as to say only buy Apple, but there are reputable and cheaper brands out there (Ravpower, Belkin, Ankar... for example) and only buy MFI certified. (They last longer too).