Opportunistic testing and out-of-hours drop-in sessions are needed because many women find it difficult to fit in an appointment around work or to find child care, according to cross-party group Demos.
The think tank said this 'would not add significantly to GPs’ workload'. Nevertheless, it suggested reintroducing incentives through QOF to fund the work.
It comes as the numbers of women undertaking regular smear tests hit a 15-year low in 2013, with just 78.3% tested.
Improving screening rates to 100% would save an extra 1,176 lives over five years and cut NHS costs by £10m a year, according to a report by Demos.
A poll of 188 women in Shropshire who refused invitations for a smear test showed that embarrassment (35%), lack of time (17%), and fear of pain (15%) were the most common reason for avoiding tests.
Extra GP training needed
The report, Behind the Screen, said: 'On-the-spot screening could help women who struggle to make appointments at a convenient time, by combining screening with another appointment, as well as overcoming the tendency of women to put off their screening by giving them an immediate opportunity to be screened – one they would find harder to evade.
'This would require GPs themselves – and not just practice nurses – to have the skills to carry out cervical screening.'
It added that all practices should give women the option to have screening carried out by a woman.
But it acknowledged the 'potential financial implications for GP surgeries'. 'We recommend that this should be recognised and offset by financial incentives given to surgeries for increasing their local screening rates.'
The report noted that UK screening rates fell after the end of financial incentives at the turn of the millennium, but picked up again when QOF indicators for smear testing were introduced for two years in 2006-7.
'This suggests that financial incentives, coupled with the other changes to GPs’ working practices, would be effective at boosting take-up of cervical screening by rewarding GPs for their efforts.'
Jo Salter, researcher at Demos and author of the report, said: 'With cervical cancer, the stakes are so high – both cost- and health-wise – but in many cases it can be avoided through screening. So it is worrying that so many women are currently ignoring their screening invitations.'
She said it was 'crucial' that obstacles to screening are removed.