Quote 1:
"You need to . . . wait 4 weeks (28 days) before booking if you've had a positive COVID-19 test, starting from the date you had the test"
Source:
https://www.nhs.uk/conditions/coronavirus-covid-19/coronavirus-vaccination/book-coronavirus-vaccination/book-or-manage-a-booster-dose-of-the-coronavirus-covid-19-vaccine/
Quote 2:
"[Q] Can a person who has recently had a Covid-19 infection be vaccinated?
[A] There are no safety concerns from clinical trials that prevent the vaccination of people with previous history of COVID-19 infection. However, there should be a minimum of a 28 days gap between the last positive COVID-19 test result and the vaccination. The reason for this is not to overwhelm the patient’s immune system, which would have been fighting off the COVID infection".
Source:
https://www.blmkccg.nhs.uk/covid-19/covid-19-vaccination-faqs/covid-19-vaccinations-faq/
As I see it, there have been more than 28 days since you tested positive, so you can therefore have your booster jab as booked.