Hi, there. Having slept on it overnight, I've got an idea for you. Do your CV as discussed. Your CV should be no more than two A4 sides in length. Then attach it to the following covering letter. I've drafted a generic covering letter for you, which you can use for other job applications as well.
[Name and address of Recipient]
[Date]
"Dear [Name of Recipient]
I'm writing to apply for the position of ________ and, for this purpose, I'm also attaching my CV.
You will see from my CV that I've gained a wide and diverse range of experience from my past and current employment, standing me in good stead for the position that I am applying for. It would be fantastic to have an opportunity to discuss with you in the next step of my application.
Thank you for reading my letter. I look forward to hearing from you soon.
Your truly
[Your name]
I know how tricky it is to look for work in the present climate in the UK, so best of luck.