What a rotten thing to happen LancsDave, just come on here to sympathise .. hope you get it fixed soon.
Have no experience of Landlords, etc., but know British Gas always treat loss of heating as an emergency as in a gas leak (wonder what would happen if you had one of these) and come around almost immediately. I do have a contract with them, but got the impression nothing to do with this. As far as I am concerned this is an 'Emergency' ..
Back to the Friday thing, have you also noticed that Solicitors send their letters out on a Friday to arrive Saturday? Became aware of this when I was going through a divorce, probably to give you time to calm down.
