One of the two Conservative candidates hoping to stand in the Rochester and Strood byelection says she supports a points-based system of EU immigration that would exclude unskilled workers like “a fruit picker in Romania”.

Anna Firth, a Tory councillor in nearby Sevenoaks, Kent, told a hustings on Wednesday night that Britain was a small island and needed a “sensible immigration system” modelled on the Australian-style system proposed by Ukip, which would only allow in people with a certain level of skills.

According to a recording of the meeting, Firth said: “I think we need the same immigration system that we have, the five points system, which currently applies to people coming to this country from outside the EU,” she said. “We need the same system to apply to those who come to this country from inside the EU.

“Once we have that system in place then I think we will have a sensible immigration policy. One that says if you come to this country with skills we really need – say you’re a brain surgeon or something in Australia as opposed to someone who has no skills, a fruit picker in Romania – then we say yes.

“If you come into this country with a job, we say yes. If you come into this country because you’ve got the money to support you and contribute to this country, we say yes. But otherwise need to say we can’t support you. That would be my policy.”

Cameron is under pressure to respond to the threat of Ukip by coming up with more radical demands to bring down EU immigration when he renegotiates with Brussels. But he has so far only suggested tougher benefit restrictions for EU immigrants and tighter controls on the numbers of arrivals from new countries entering the EU, which falls well short of Ukip’s points-based policy.

Firth’s comments demonstrate the pressure on Cameron from within his party to respond to Ukip leader Nigel Farage’s much tougher promises on immigration.

Ukip’s candidate in Rochester and Strood, Mark Reckless (left), campaigns with his party leader Nigel Farage last week. Photograph: Andy Hall

Speaking with both Tory candidates in a village hall near Rochester on Thursday, Cameron signalled he would be unveiling an extra crackdown on EU immigration beyond measures already announced, but would not be specific about the plans.

He said current Conservative proposals included “things like abuse of the benefit system, including making sure that when new countries join they can’t all come here and also further action in addition to that to make sure we have more effective control of migration”.

In a subsequent television clip, he said: “We will be setting out our plans in due course.”

The Times reported that one option under serious consideration was to demand from Brussels an “emergency brake” on the number of migrants from particular EU countries on the grounds that further influxes would put unacceptable strains on public services and social cohesion. This would be seen as a middle way between Farage’s plans for restrictions based on skills, or London mayor Boris Johnson’s call for quotas, and the less tough option of more curbs on claiming benefits.

Firth set out her support for discriminating against EU immigrants based on skills at a public meeting in Rochester on Wednesday night, where she appeared alongside fellow candidate Kelly Tolhurst, a local councillor and director of a marine survey firm.

National media, including the Guardian, Telegraph and BBC, were banned by Conservative officials from reporting on the hustings – a move described as wrong by Sarah Wollaston, the Tory MP for Totnes, who was also selected via open primary. However, the Guardian since has obtained a recording of the event.

During the hustings, Tolhurst struck a tough note on immigration, saying she would be firm about letting Cameron know the problems it caused in Rochester, and added that she would push him for a new hospital for the area.

The candidates mostly spoke about local issues but residents also asked for their views on national subjects including the erosion of civil liberties in the case of the former Guantánamo inmate Moazzam Begg and disillusionment with Westminster politics.

They both described themselves as Eurosceptic, while believing it was the best thing for the country to let Cameron renegotiate with the EU before holding a referendum. They also each listed their priorities as improving the local hospital services, raising standards in schools and protecting the area form unwanted development.