Personally I would just get an ebay engine for £300 and fit it over a weekend.
If you cant DIY I would cost up options;
sell as is
fit second hand engine you supply
fit engine garage supplies
fit recon engine
etc
If you can only sell it for £1k as scrap, but can get a used engine fitted for £1k, then at least you would have a running car that is hopefully worth about £3.5k (or could be throwing good money after bad if you are unlucky)
You can get a second hand engine for one of those for £300-£400. Depends whether the garage is willing to fit an engine they do not supply, and your appetite for risk. If you supply a duff engine you are out the labour.
You might want to consider the cost of fitting a new belt to a second hand engine as part of your cost calculations as well.