India by 2014 may have an internal market worth £352bn. This would be much less than China's £975bn consumer market in 2008, but a lot of Indians speak English so it's understandable the government of the day up-sticks and moves to Bangalore even if a slice of the Shanghai pie is bigger. In return, India would like Indians to be able to move to Britain to work, learn and use the NHS - that's something not so easy to do with the European Union cap on non-EU migrants.
Nethertheless there is something Britain can do to put India in our gratitude. Help keep the new trade route with north Afghanistan open. India wants to put Tajik north Afghanistan in its geopolitical pocket. This as much to challenge Chinese influence in Central Asia as anything to do with Pakistan - serious Indo-Pak conflict, beyond posturing, being essentially over for now.
Indeed, as the once great power which drew up the lines in the region, the British Commonwealth is arguably a bridge between the two old feuding sub-continent states. Anyhow, now they both possess nuclear weapons, I believe the Indo-Pak elites have also recognised wider war is futile and have decided on putting partisan objectives before national ones. It worked so well in Western Europe.
The British role involves squaddies jumping on IEDs on Afghan roads so the trucks can pass through, or just by hanging around to make an obstacle of themselves to any organised Pashtun move on the more developed north. But you say Pakistan doesn't seem to get anything out of this deal - it's just a "Afghan-Britain-India" nexus,will never happen - not quite. Prediction: Pakistan will be given "Pashtunistan" or a Pashtun state will be created under the wing of Pakistan.
Pakistan will get their "strategic depth". Indians will be able to develop and advance on Central Asia. British NGO workers will get their paid
The ethnicity map below is from this Stratfor article by the excellent George Friedman (who hasn't yet, to my knowledge, written about the Afghan-Britain-India nexus). There are many available on the net but this one is particularly clear and colourful.
The Pashtun are coloured orange, Tajik and Uzbek in the north are green and brown respectively. The trade route from Afghanistan to India goes through the Kyber Pass, directly East of Kabul on this map. The Pashtun region being coloured entirely orange glosses over its social complexity. Pashtuns are riven by tribal divisions (e.g. Durrani vs. Ghizai) and by cultural rifts between their few urban settlements, the rural farmers and the Pashtun nomads.