From Jeri's link:

"If you recently had COVID-19, you may consider delaying your next vaccine dose (whether a primary dose or booster) by 3 months from when your symptoms started or, if you had no symptoms, when you first received a positive test.

Reinfection is less likely in the weeks to months after infection. However, certain factors, such as personal risk of severe disease, or risk of disease in a loved one or close contact, local COVID-19 Community Level, and the most common COVID-19 variant currently causing illness, could be reasons to get a vaccine sooner rather than later."

The caveats in that extract, which I won't bother to highlight as we can all read, in no way amount to a recommendation that "there is a good reason to wait 4 months or more after having Covid or a Covid vaccine, to get a booster." I haven't found any source on any UK website that suggests such a delay, and I did go to the trouble to try to find one.

In medical matters, it's often the case that we should not make recommendations in these threads as to how people should act. Drawing attention to reputable sources to support a point of view is valid, but "nuff said" doesn't cut it.