The UK’s Foreign Office’s travel advice states:
Local travel – North
The security forces have imposed restrictions preventing all foreign passport holders (including British nationals) travelling to the Northern Province. All foreign passport holders planning to travel to the north must get prior approval from the Ministry of Defence.
You should send a written request to the following address/fax: Secretary Ministry of Defence & Urban Development (Attn: Military Liaison Officer) 15/5 Baladaksha Mawatha Colombo 3 Fax: +94 11 2328109
Military activities are ongoing. You should obey orders from the security forces and signs warning of the danger from land-mines.
Foreign media crews will still need prior permission to travel to the Northern Province. Travellers to the north may also encounter further restrictions, including around military establishments and areas where demining operations continue. For more information about the accessibility of a particular area, contact the Sri Lankan Military Liaison Officer on +94 11 2436 019.
Local travel – Jaffna Peninsula
There is free movement everywhere outside High Security Zones with fewer checkpoints around the Peninsula. Operations to clear mines continue, particularly in the heavily mined area towards Elephant Pass.
Local travel – Kilinochchi, Mullaittivu, Mannar and Vavuniya
There is a continued heavy military presence. It’s generally possible to move around freely, although some checkpoints remain (notably Omanthai). There was severe war damage to property throughout the northern region so accommodation options and infrastructure are limited. Some areas were heavily mined and operations to clear minefields continue. There are signs warning of mined areas but you should take care.