I am spending time in England and staying in Wembley
visiting friends on 4 - 5 days in a row and using the london underground - within london and outskirts
My question - Do I buy a daily pass, or am am better of getting another pass that will allow me to travel cheaper for 4 - 5 days.
I will be using the underground just twice on all 5 days. Advice much appreciated
Neither, buy an Oyster card when you arrive. Fill it with some cash and refill it if it gets empty.
You can use this on all trains and buses in London. There is a "cap", you never pay more than the daily pass cost, once you reach that all further trips that day are free.
When you leave you can cash in your Oyster card and get the deposit and any remaining credit back.
Alternative, if you have a credit or debit card which supports "contactless", you can use thta directly. Same cap applies.
Info here: https://contactless.tfl.gov.uk/
More info on the oyster card:
https://www.londontoolkit.com/briefing/oystercard.htm
You are out in Zone 4. A week travelcard for Zones 1-4 is £50.50; a day's cap is £10.10 on Oyster so for 5 days there is no advantage. If you are really only going to make one trip in and one trip out to Zone 1, with no other travel, then you would pay £3.90 peak and £2.80 off peak.
So Oyster PAYG (or contactless payment) makes the most sense, including your Heathrow travel.
I agree with the recommendation to just get an Oyster and load it with some money (say, £40-50). If it runs low, you can top it up at any time.
Just to make it crystal clear why this is the best plan (I know it's confusing):
If you use an Oyster and travel less than the cost of a day pass for the zones you travel in, you pay less.
If you use an Oyster and travel as much or more than the cost of a day pass for the zones you travel in, you pay the day pass cost.
So, with an Oyster, you either pay less than a day pass or the same as a day pass, depending on that day's total travel. You never pay more than a day pass would have cost, but you don't have to know in advance what your travel will be, and you aren't penalized if you "guess wrong" at the beginning of the day. You can't lose.