The British derive their power from their relationships with some very dubious groups, whom they host in their own country, and the potential these groups have to cause trouble in their native country. This power is not all that different from what Pakistan wields, as a haven for terrorists. In Britain's case, they have a far bigger ability to mold public opinion through the media, so nobody has the ability to put make the blame stick on them. These terrorists are also presented as simply freedom fighters, or as political dissidents, etc. The British support the Pakistanis because on this issue of extortion and pressure politics both think alike. Both have deep fingers and tentacles in Sunni extremist politics.
The above would however not be sufficient. The British also like to piss on the deepest wounds and weakness a country may have. In our case, it is Kashmir. They like to be present themselves on a pedestal and play the judge in disputes, making sophisticated assertions of fair play, pleading friendship but always batting for their favorite side, the Pakistanis. The Indians get fooled by hints from the British, that the problem is not their support for the Pakistanis or Muslim appeasement, but our inability to present the facts properly. Next time we try even harder, in a court set up by them. No amount of terrorism rained down on India would even move them in the slightest. They will come forward with their homilies, and we will be expecting them to finally take the side of the victim, but they will again hurt us by suggesting that we are ourselves responsible for the terrorism, that we need to deal with root causes, with core issues.
Most of all, the British get their power from their hold over the financial markets, the banking system, etc. They get their power from having their fingers in every economic pie. That is why Iran and Russia irks them so much. These countries deny them a say in their local economies, and that is why the whole might of the media and public opinion needs to be brought against the Russians and the Iranians.
India has opted to buy peace with them on their terms. What India needs to do is to play divide and rule. We should continue to increase our economic relations with USA, but demote our political and economic relations with the British, or at least hint at degrading. The danger of losing such a huge emerging economy would be a hard blow on UK. India has a perfect foil, "We are a primitive nation and susceptible to emotional outbursts, and it is UK's job to appease us. Otherwise no deal". We should not be looking to cut off all relations with them, or to become their enemies or even adversaries. We should be aiming for a state of affairs, where there is always some tension because of historical wrongs committed against us, and the British are forced to make concessions to assuage our 'feelings'. But no matter how much they try, their 'success' in assuaging our 'hurt feelings' should be temporary, and we should fall back on the rhetoric of historical wrongs. India needs to increase the cost for the British to keep on trading with their old colony.
END OF RANT
What we could do:
1. Dissolve the Commonwealth. Promote NAM instead. Also make India-Africa, and India-Caribbean summit a regular affair.
2. Find new partners in EU, partners like the French, the Germans, the Spaniards, the Greek, the Irish, the East Europeans. Downgrade India-UK dialogue.
3. Never let anybody below the British PM to meet with the Indian PM.
4. Never take British politicians or British royalty around India to do Imperial Tourism, or even to besmirch the memories of those fallen in our battles against the British, like to Jallianwala Bagh!
5. No place in India should carry the name of any British royalty or British Viceroy or anybody below.
6. Never talk to the British about the Indian Subcontinent or our political problems with Pakistan. We don't want their sympathy. We don't want their understanding. We don't want their judgment. If they show their sympathy for Pakistan on Kashmir issue, hang another set of boulders of colonial sins around their necks, and downgrade relations with them, e.g. for not responding positively on the question of 'compensation' or return of historical artifacts. Send a UK diplomat packing.
7. If they step on our toes, never hesitate to send a British diplomat packing.
British loss of influence in India would make the Americans lose their trust in UK's worth, making UK slide even further down the power ladder.