Thats all very straight forward then.
Call Cov and head for Draycote Water VRP. They will ask you to report at that VRP inbound. Probably give you a sqwark regardless of your service needs. It gets busy at Draycote so keep a good look out for inbounds and other passing traffic going elsewhere.
From Draycote, the norm is to head North for a south westerly 23 arrival.
No need to talk to Brum........
Inbound, their controlled airspace base near Draycote is 3500, so don't worry about that and you should be well under the 2000 base and well inside the Charlie Tango NDB.
Outbound, just be mindful on departure of the 1500 base inside the zone and stay with Cov Radar all the way until clear to the East.
If in doubt ask them. Good Controllers at EGBE.