Which bank account would be the best to open in London and transfer and convert SGD into GBP from Singapore at the cheapest rate?

I'll give you the JiPay paynow app https://www.jipay.app/cards-for-helper, they have different offers for transferring money abroad.

Yes there're a few HSBC branches in London. You probably don't need to open a London bank account unless (1) you plan to buy a car - some dealers want UK bank transfer - or (2) you need to pay for accommodation via UK bank transfer. But even for that, there's DBS remit - you can do overseas bank transfers with zero fees for selected countries and their native currencies. UK is included, I just paid for a bill a few months back with DBS remit to test it out.

You can open an HSBC Everyday Global Account (EGA) in SG. You get an HSBC EGA debit card which allows you to withdraw cash overseas and also pay for contactless purchases, zero fees. Depending on the tier of banking you register for (Advance, Premier, Jade), you might need to either maintain a minimum account balance ($30k? I think?) after 24 months or perform monthly recurring transactions into your account. Bonus: if you register for HSBC Advance banking, you get their HSBC Advance credit card which offers 2.5% cashback, 3.5% for spending over $2k (handy if you're going to use it to pay for school fees, accommodation etc). Annual fee waived perpetually for Advance banking members. Find out more about HSBC EGA: https://www.hsbc.com.sg/accounts/products/every...

UK is going contactless with a lot of things now so most retail can be paid by contactless payment, it's unlikely you'll need cash much.

Do check out Youtrip as well. Singaporean company. It's a multi-currency wallet allowing you to store up to $5k SGD and convert at very competitive FX rates. I use it currently and the rates are more or less at market rates. Find out more about Youtrip: https://www.you.co/sg/

I use Youtrip. It's very good. For your consideration​​​