I have used 2 exchanges:

1. BitPanda -I used this company because they offered the option to pay by credit card. They have a horrible verification process where you have to hook up on video with a 3rd party agency and get verified. They make you hold your passport up to the webcam, take pictures of you and your passport and ask why you want to buy bitcoins!!! I personally wouldn't use them again as I ended up paying a ton of fees because I used my UK credit card  (MBNA). I was charged an extortionate amount of fees by MBNA - £118 "Cash Advance Fee" as this site is considered a gambling site and £66 for foreign currency transaction plus a crappy exchange rate!!! However, If you live in the EU or have an EU account, they are pretty good - apart from the verification process

2. Coinfloor.co.uk - I used them today with the intention to buy some bitcoins. You need to get yourself verified - copy of driving license (or passoprt). Verification took a couple of hours. I transferred funds from my HSBC account to their GBP account in Poland. HSBC fees - £4 and Coinfloor fees £5. The site states that transfers can take between 1 - 4 business days due to overwhelming demand. My funds got transferred within an hour!!! I give coinfloor 5/5. I haven't bought my BTC yet, I'm waiting for the price to drop further. You can transfer in USD, EUR, GBP and a load of other cryptos. The only downside is that the minimum deposit amount is £2500.


There's also cex.io but their fees are higher than coinfloor and they have closed new registrations. But, I don't think they have a minimum deposit amount,

Hope that helps.