The trouble is places such as East Midlands and Birmingham do not always have the capacity to provide a service for many light aircraft. It is made worse by fewer radar services these days what with Cottesmore and Coventry RADAr that have now gone.
My advice is in the instance you mentioned and if EMA was not too busy, it is probably wise to get a service. The lookout is all very well, but it is all too easy to miss another aircraft. If they cannot offer you a service, they will tell you.
One final point is, keep the R/T Short, so make the intial call Brief as follows:
'East Midlands, G-ABCD' then wait, then when they contact you, do not give your life story. Again keep it brief and say what you want. You can cut out terms such as 'at this time' because if you say for example you are over Ruland Water, you do not need ' at time' that will be obvious.
ENDRES, you did not say how experienced you are, but the more you get up to speed and confident with your R/T, the more likely you are to get the service you wan't such as radar, zone penetration or zone ransit.
One final thing, is London Information can be useful, but perhaps under used, but is useful in remote areas, for a basic service and it is usually not busy, it also has the benefit, that in the event of deteriating weather and an unplanned diversion, you can request TAFs, Actuals, check when the airport closes, even request for it to stay open, even file flight plans. You probably need to look this all up.
Below is a link:
https://publicapps.caa.co.uk/docs/33...ServicesIF.pdf