Theo wrote

I need to move some heavy appliances - washing machine, fridge freezer
etc - by a few dozen metres (hard surface), including over a door sill.

Can anyone recommend what's the best way to do this without getting
someone else to assist? Obviously I don't want to damage them.

I once had a washing machine delivered and the sole delivery
guy managed to manhandle it out of the tail-lift van and into
the kitchen using just a 'sack barrow' kind of thing.

That’s what I use, it works fine.

Would something like that be worth using

Yes.

(what sort should I get?),

Mine has inflatable tyres which isnt idea,
it needs to be pumped up before use but
got borrowed and the borrower burst one
of them and replaced it for more than a
whole new one costs and now only one
needs to be pumped up before use.
The solid tyre ones don’t have that
problem but don’t work as well over sills.

or are there any better ways?

Not with just one person moving it with that door sill.