1. Agree with just pumps.
2. Following that solution you would need the stub of copper to connect the compression end of the new flexi.
3. That type of (normal) isolation valve is designed has compression fittings each end. These have a 45 degree internal chamfer at the end, into which an olive fits and is compressed when the nut is tightened. Because of the chamfer, these usually have a fairly sharp "vee" at the end of the threads. The sharp vee can cut into and damage the seal inside a female flexi connector.
4. Because of the above, If you got a flexi of the right length with 1/2" BSP female connectors each end (e.g.
Screwfix item 50739) you should not fit it directly to the isolation valve. You have three options:
4.1 Change the isolation valve to one with a flat end. You can get them from Toolstation. I don't think
Screwfix do them. However, you would have to isolate the water flow elsewhere to remove the old valve.
4.2 File the end of the existing isolation valve flat. Personally I wouldn't risk doing this in-situ.
4.3 Replace the stub of copper pipe with an adaptor such as
Screwfix 2665R. You would need a new olive to fit it under the isolation valve compression nut. I prefer copper olives, but
Screwfix don't list them. You could probably buy the cheapest 15 mm compression fitting and use one of the olives from that.