[Thephoenix572]

Any ideas where I can buy a cheap but good quality hand propelled lawnmower, the kind that is not electric

[arugula]

If you google you'll find that you can buy a Qualcast (good make) or a Bosch (don't know why they make one without a motor or engine) for about £40 from places like Amazon. You might be able to buy one at a local garden centre or similar to save paying carriage...

[Kleftiwallah]

Look in the pages of the local rag for garden machinery repair spots.  I bet they will have a pushalong that they have repaired and the owner has gone electric and not bothered coming back to pick it up.   

Cheers,     Tony.

[Gwiz]

"Webb" lawnmowers still make a cheapo roller push mower, and have a look at "Handy" products they own the webb brand and market the same mower for a few pounds less.
(I've deliberately suggested these two as they are roller mowers which are far easier to use as you can go right over the edge of the lawn with them, with the wheeled type you can't do this)