If you buy tickets each day they will cost £2 each way. £2 x 10 = £20

If you use Oyster prepay you will pay a £3 deposit and the tickets will
cost £1.70 each = £17 + £3 = £20

If you buy a weekly ticket on Oyster for Zone 1 it will be £18.50 and
there will be no deposit (a special offer at the moment) = £18.50

Do LUL still do Zone 1 Carnets - if so, how much do they cost? (but see the
response that advises a Travelcard season).

Tube carnet (being withdrawn from January) is £17.

Miss Uk Railway wrote:
This week, I'm travelling from Rugby to Euston and back with Virgin
every day. I will then need to make a daily return trip from Euston
underground to Westminster underground.

Would it be cheaper to buy 5 x daily zone 1 return tickets or an Oyster
card? I've no idea how Oyster works - can I buy it at Euston tomorrow
morning and do I simply put money onto it, i.e. pre-pay? Does this
method work out cheaper than buying ordinary single/returns?

Others have answered your question. I'd say that (as a Oyster card
owning visitor to London) if you're going to visit London more than
about once a year an Oyster card is a Good Thing to have. It'll save you
time and money.