the first step is to clarify the airspace situation, so in respect of Coventry, revisit your statements about "within...control area" and "CTZ".
I'll rephrase, the light blue bit on the chart.
All depends on your intended route and intentions. Provide some detail into that and we can answer your question.
Assumng Cov is your intended destination here and is not be used purely as an example. You can easily fly in without speaking to Brum (maybe use their listening sqwark) and in so doing, avoid the base of Brum's nearby controlled airspace. That would suit all parties I'm sure.
I'll be coming from Cambridge, and pretty much a straight route West, so I guess that as long as I'm below 1500' as I get there (which I would be anyway), there won't be a problem?