I have no idea if the Peatol UK distributor (Peatol Machine Tools) is still working. However I have successfully bought parts and accessories (recently) direct from Taig in the US. They are very helpful and very responsive to E-mail queries.
Shipping gets expensive, and you are stuck with the dreaded VAT and duty, but it does work, and the parts and accessories are surprisingly cheap but high quality. Parts & Accessories Archives – TAIG Tools
They do a three jaw self centring chuck with machinable jaws, and four jaw independent and self centring ones.
Arc do Peatol (3/4 x 16 tpi UNF) backplates that will allow you to put their small chucks on as an alternative.
Sherline chucks have the same UNF thread, and can be bought from MillHill supplies in the UK, but they need a seating register between the chuck and the spindle face (you can find the details of making one online) .
One last thing – do check that the spindle nose thread is actually 3/4 x 16 UNF. Taig do a version of the spindle that takes ER16 collets ( which is what I have) and that has an M22 x 1.5 thread. If it's a fairly old unit it will most likely be the UNF one. But if you have got an ER one , buy a set of ER16 collets and use them. I do have 3 & 4 jaw chucks, but they only appear when turning something bigger than 10mm otherwise the ER collets are far nicer to use.