The fact that a majority of MPs backed David Cameron's proposal to extend airstrikes to Syria in targeting Islamic State (Isis) could have given the prime minister a long-term boost to his efforts to renegotiate Britain's relationship with the European Union, a leading thinktank has said.

Hours after MPs voted 397 to 223 to approve the bombing, Cameron flew to Sofia to press the case for EU reforms with Bulgarian prime minister Boyko Borissov, which will include the UK being able to curb workers coming from poorer EU states. The Guardian reported that Cameron wanted the 27 other European heads of government to accept his terms by the European council summit on 17 December 17.

Nina Schick, from the thinktank Open Europe, which campaigns for EU reform, said the victory in the Commons would give Cameron more clout in his talks with European leaders – in particular with France, whose leader was uneasy with British demands. She told IBTimes UK: "It won't have a direct impact on the content of the negotiations because what Cameron is trying to negotiate has already been laid out.

"But it will have an indirect impact in that it might increase good will among EU partners to reach a deal with Cameron, particularly for France, because the vote really is a sign of solidarity. It will also more importantly serve to remind the rest of the EU that the UK is one of the leading foreign policy powers in Europe. At a time when the European neighbourhood is in flux, it will serve to remind EU members that a Brexit would be quite detrimental."

Among Cameron's demands, which he outlined in a letter to European Council President Donald Tusk, the prime minister wants controls on immigration, guarantees of member state sovereignty and cutting back on red tape in business. Schick said British demands for an opt out led to "acrimonious" relations with Brussels, but in light of the Greek and migration crises Cameron has been vindicated. "It will help bridge that gap where political good will was lost over the summer. I think other member states may think that a Brexit is not a risk they are willing to take," she said.

However, the head of the Berlin Office of the European Council on Foreign Relations, Josef Janning, told IBTimes UK that helping France tackle IS and renegotiating Britain's EU relationship were two different things in the eyes of many EU policy makers. "Merkel and Hollande have a genuine interest in keeping the integrity of the EU's political framework, and they see Cameron's demands as undermining this," he said.

"So, they could be won for additional exemptions for the UK but will resist treaty change because of the contagious effect it will have on others. Cameron wants to weaken the EU at a time of its weakness; that is not something Merkel or Hollande are interested in. Also, they know that a Britain that is staying in the EU will be a status quo player, opposed to anything which reads like more Europe."