if your looking for a service to swap FIAT ($£Euro) expect KYC, as these are called exchanges.
just dont pretend /treat these exchanges as 'wallets' .. move funds away from exchanges.
if you are just looking for somewhere to store bitcoin (a wallet) then all proper 'wallets' are KYC free.
there are webwallets. but most have it where THEY hold the private key (secret to spend the funds) and you have to rely on them 'managing' it on your behalf.
some webwallets are also exchanges. but some are not exchanges..
some webwallets also allow you access to the private key..
but most peoples rule is dont use a webwallet for any large amount. and especially dont hold for a long time in a webwallet.
and if the webwallet is also a exchange. expect KYC and more risk of them running off with your funds at some point.
there are many personal wallets such as lite-wallets like multibit/electrum which allow you access to the private key so that YOU hold the secret to spend the funds. and that private key is stored on your device.. not some website
then there are full node wallets which is where your computer is helping the network to protect everyones funds. and that private key is stored on your device.. not some website
then there are hardware wallets which is where a separate device(imagine pendrive/external hard drive) that the private key is stored on. but then requires a personal wallet on a computer or a browser extension on a computer to connect to the device to spend it
now you have learned the basic lessons
https://bitcoin.org/en/choose-your-wallet