People aged over 70 and those with long-term health conditions would have access to the same named GP for every appointment under plans unveiled by the Liberal Democrats, as polling reveals almost half of Britons rarely or never see their family doctor.

The Lib Dem leader, Ed Davey, said the policy would require 8,000 more GPs and take at least four years to implement at the cost of an extra £1bn a year, with the money coming from taxing big banks.

Elderly people and those with long-term conditions, including mental health conditions, have been found to benefit the most from access to the same GP, the Lib Dems said, pointing to a study that found people who have kept the same GP for more than 15 years have a 25% lower chance of dying than those with a new GP in the first year.

Polling commissioned by the party found almost half (47%) of UK adults who have seen a GP more than once in the last couple of years say they rarely or never see the same doctor for each appointment, , with almost one in five (18%) saying they never do. This latter number rises to 27% among people aged over 65.

Davey said: “It is a scandal that under this government’s watch the family GP has become a thing of the past. Pensioners are not receiving the care they need because doctor surgeries are swamped, leaving waiting times spiralling out of control. We need a return to the family GP, starting with older people and those with long-term health conditions.

“We want to see the return of the named GP, so patients with complex care needs see the same GP and don’t have to waste time going over the same details every time they see a doctor. This would provide vital personalised care for those who need it most, helping people lead healthier lives, independently in their own homes wherever possible.”

The region worst for people never seeing the same GP for every appointment is the south-east of England (25%). The polling also found almost half (46%) of adults say the wait to see the same GP is now considerably longer, rising to 55% of over-65s.

Davey told BBC’s Sunday with Laura Kuenssberg programme: “All the evidence shows [having a named GP] improves their health outcomes; it actually saves the NHS money because people don’t go into hospital so often, so it’s a really sensible policy.

“You’re right, others have promised it before – Jeremy Hunt [the former health secretary, now chancellor] did – but I’m afraid what they implemented was a sort of tick-box exercise; it’s not been implemented. So many people complain they don’t see the same GP.”

Asked how it would be funded, he replied: “We have said that the tax cuts that the Conservatives have given to the big banks since 2015, they should be reversed. That’s worth £4bn a year, not just to pay for this part of our policy but for many other parts of our healthcare policy.”