MPs could get police protection at surgeries following the murder of Sir David Amess.
Home secretary, Priti Patel, said police guards for politicians at public meetings is one measure being considered as part of a review into security for MPs.
Sir David was stabbed to death while meeting constituents in in Leigh-on-Sea on Friday. Ali Harbi Ali, 25, has been arrested and being held under the Terrorism Act 2000.
Councils have been paying tribute to the dedicated and widely-respected MP.
Cllr James Jamieson, chairman of the Local Government Association, said: 'David was a dedicated MP who worked tirelessly for his constituents and on behalf of everyone in Parliament. As Chairman of the Fire and Safety APPG, he also worked hard alongside many, including councils, to try and improve fire and building safety - a crucial piece of work for so many.
'Everyone in public life should be able to go about their daily business without fear of attack. To lose his life in such terrible circumstances is tragic.'
Cllr Tony Cox, leader of the Conservative group on Southend-on-Sea Borough Council, said: 'We are all shocked and saddened by the death of Sir David Amess. He was a great man, a great MP, a respected parliamentarian and respected by his residents. What we cannot lose sight of here is that a wife has been robbed of a husband and five children have been robbed of a father.
'He was a passionate believer in the right of life and it's poignant that his life has been so cruelly taken away. Our thoughts are with his family and friends at this sad time.'
