> This doesn't sit right with me. If someone comes in with thousands of pennies am I allowed to refuse that type of payment?

In the UK yes.

There are rules about the maximum you can pay in different denominations.

    1p – for any amount up to 20p
    2p – for any amount up to 20p
    5p – for any amount up to £5
    10p – for any amount up to £5
    20p – for any amount up to £10
    25p (Crown) – for any amount up to £10
    50p – for any amount up to £10

People where paying their council tax (think of them as state taxes) in 1's and 2's.

If you wonder what 25p (Crown) is, the law dates from the early 70's which was the era we went over to decimal coinage.