Say I want to settle a debt of 0.22p.....
0.22 of a penny is £0.0022.
You can't pay someone a fraction of a penny. Debts that involve fractions of the smallest currency are usually rounded to full multiples of the smallest unit. E. g. if your phone company charges 1.79 ct. for a one-minute call, it would be rounded to 2.00 cents.
Unfortunately shops/banks and the like have the right to reject this sort of thing I think but the law might have changed since I last looked.
I think there's a difference between banks and shops. If you actually happen to sit on a large amount of coins (e. g. because you're running a grocery store and all customers pay with coins), then the bank is supposed to be the place where you deposit them. Some banks also encourage their retail customers to deposit the content of their piggy bank to their savings account. Naturally, they don't like to count that by hand which is why large branches often have counting machines for that purpose. The small branches, however, often don't have counting machines so they have to count coins by hand.
However, in most jurisdictions, legal tender doesn't mean that people have to accept absolutely anything that is legal tender. For example, vending machines never accept 1ct and 2ct coins; Given that all vending machines work like that, I would doubt that this practise would be declared illegal in court. However, in Finland, stores have to accept 1 ct and 2 ct coins even though such small coins are not used in Finland. Most people use to throw these coins into the trash because they don't know what to do with them; The postal service however, uses to ship their 1 ct and 2 ct coins to Germany in order to get rid of them.
By the way, you don't have to use cash in order to piss people off. I recall that there was a case over here in Germany where someone was angry with his lawyer (probably because he lost a case). So he chose to pay his lawyer with ~20 000 wire transfers, each amounting to 1 cent. The lawyer was charged €2.50 for each of these transactions. (The client probably had an account with unlimited free wire transfers.) Now the lawyer reacted to this payment by sueing his former client. He won the case; the court decided that what the client did was an "immoral damnification". He was ordered to compensate the transaction fees he had caused, which he also did. He refrained from splitting up that transaction as well.