Be sure to check whether VAT applies to your quote or not – if it does apply, the price will go up by a further 20%, if this has not been included. Take this into account when comparing quotes.
Ask if any or all of the work is covered by a guarantee and how long it lasts. Check if any components supplied (e.g. a boiler) are covered by a warranty, and for how long.
If the price from your preferred plumber is higher than you can afford, talk to them to see if there is any way the price could be reduced. Don’t agree to start the work until you have agreed that the price quoted is acceptable.
If it is a big job, make sure start and completion dates are included on the contract.