You would pass through immigration and then after getting your bags pas through customs but only if your bags aren't checked through. If your BA/VS flights are on the same ticket then they should be but not if they are separate bookings.

If your bags are checked through then use the airside bus from T5 to T3 where you will pass through security (but not immigration or customs) and then be airside at T3 for either main departure lounge or the VS clubhouse (only if you are flying UC or are AU in flying club - you don't state which you are)

In those circumstances there is very little reason to use the UC wing.

There are essentially two parts to the UC wing - again for UC passengers or AU in flying club - (1) for those arriving by car / taxi where the usual check in formalities are done before passing through the private security channel and (2) for those checking in at the UC desks downstairs who only use the private security channel. The wing is not a place to linger- they don't serve drinks or anything like that.

If you want to pay for an uber just to use drive through check-in then that's up to you but as you are arriving from a fliight at LHR there really is, IMHO, little point.