Update: I removed the screw on the front of the pump again, and the screw inside still would not budge. So I used the screwdriver and a small hammer and tapped a few times. I could feel it was moving a little, then I put the screwdriver in the center and I was able to move it more. I then put the central heating on and turned the screwdriver a couple of times and I could feel the motor going. I then put the outer screw back on.
The heating has been working for the last hour or so and I have hot water and heating again (for now anyway!). Thank you again everyone so much for your help!
What do you recommend I do now? Should I consider replacing the pump, or leave it. How long is the pump likely to last? The central heating system was installed around 7 years ago.