And now the letting agents are claiming the plumbers are lying to us about how long it will take to get parts in

They've told us 3 weeks, but apparently they've told 1st lets 7-10 days.

Before I do anything I'm going to wait until I find out exactly how long it takes.
A measure of how helpful the agents are prepared to be with us should be gained when we contact them to try and get a receipt for the washing machine. That's being done by email in the first instance (since they seem to favour contacting us that way now) but they were pretty resentful at us mentioning it having flooded in the first place (it was bought a month before we moved in) so I guess we just have to hit and hope. It's a £96 call out charge if we can't get it so obviously we're not ducking out of getting onto them over this.