Having read a little about the battlegroup concept it seems like an EU/Labour invention to provide rapid reaction formations lifted from the WW2 German idea. Surely though the point of the regimental system is to generate an esprit de corps which must be diluted with battalions being sent off to disparate battlegroups all over the place?
Battalions form part of Regiments, the esprit is at battalion level. Take the Paras for example, 1, 2, 3 & 4(V) Para have there own unique character, celebrate separate battle honours, wear different DZ flashes, they are fearlessly proud of both their regimental and battalion histories. Typically only 1 Para battalion will form the core of a combined arms battle group in A-Stan, supported by airborne gunners (7RHA), engineers (9Sqn) and Cav (HCR) etc. Not being part of a full Regimental deployment in no way impacts their esprit or loyalty to cap badge.
The Regimental system was designed to allow for one battalion to be deployed overseas (Rifles deployed for five years without a break during the Napoleonic Wars), with at least one sister battalion at home recruiting and running the depot/Regimental HQ. Over time training was consolidated in to centralised locations grouping infantry, armour and trades at specialist depots. Trained recruits are fed to their desired Regiments after basic for further role specific training (light, medium or heavy role) and integrated into the historical culture of the unit (guards, para, line infantry), learning the traditions, marches and battle honours. The Regiment you join can be heavily influenced by the recruiting office, the recruiting Sgt can be very convincing! You may enter wanting to join the Guards and end up walking out scratching your head signed up for the Lancers.
The battle group system is all about flexibility, which has allowed the UK to keep a division worth's of assets deployed non-stop on operations for over ten years in Iraq and A-Stan. Quite and achievement for such a small military.