David Cameron's faith in the "big society'' is to be put to the test after Oxfordshire county council announced that professional staff are to be removed from six libraries in his Witney constituency, leaving them to be staffed by volunteers.

The culture minister Ed Vaizey will also see two libraries in his neighbouring constituency of Wantage stripped of staff by the Conservative-controlled county council, leaving a mix of volunteers and professional staff to run them.

The council has decided to keep only 22 of the constituency's 43 libraries fully staffed, but had planned to close 20. Cameron will be relieved that libraries are to be kept open in Banbury, Chipping Norton and Witney within his constituency.

Oxfordshire council insists it did not make its decisions on the basis of political lobbying by prominent local MPs, but according to where people live, work, shop and study.

There will be a four-month consultation on the libraries plan, with no changes until the start of the next financial year in April.

The initial plan to close libraries outright led to a wave of protests including some involving authors such as Philip Pullman, Colin Dexter and Mark Haddon.

The shadow libraries minister Gloria De Piero said: "Volunteers have a role to play in libraries, but I would be amazed if you could run libraries by volunteers alone. It is a professional job.

"I have asked Vaizey whether he has any plans to run the House of Commons library through volunteers, and he has not replied so I presume he realises he does not."