Taking cash to the UK and France

How much money do I need to bring with me to London so my entry won’t be denied?

There is no set amount.

I believe what the officers want to see is that you are a well-prepared traveller who is able to pay for their food, accomodation, onward travel costs and small emergencies without recourse to public funds.

I am not an immigration officer, but as an ordinary citizen I would take enough cash in sterling to be able to pay for taxis, meals and at least one nights accomodation. The remainder of the anticipated cost could be in travellers cheques or, more likely nowadays, be in a bank account for which you have a Visa or Mastercard affiliated debit card which is usable in the UK.

The question of cash or not is likely secondary to whether you can demonstrate that you have access to sufficient money for the planned duration of your visit and, if they are concerned, whether you can demonstrate that the money actually belongs to you and is available for your use (and not for example a sum lent to you and due to be repaid soon)

if it can be either euro or sterling.

It would be prudent to have some sterling or a good plan for converting some Euros to sterling at the time and place of arrival. I expect immigration officers prefer to see this sort of prudent planning in visitors.

When possible, use credit card instead of cash. For a short trip like yours, a credit card can already establish the fact that you have money to support your trip. In fact, in most situations they may not even check. I would suggest you get some cash in both euro or sterling before you travel, but not a lot. Something that can cover some basic food and urgent needs, as well as situations where only cash is accepted. Then bring a credit card.

Bringing a lot of cash is never a good idea when travelling. Depending on the country, there is an upper limit of cash you can bring in before you have to declare it. Not to mention walking around and flying with a lot of cash is quite dangerous.

When it comes to minimum, there is none. You don't have to bring any if you don't want to. You just need to have something. If you only want to use credit card, just bring your credit card. If you only want to use cash, bring cash that would cover all your expenses. But, if the officer asks you for your source of funds and you tell him/her "I got nothing", that will be a problem.