Vast majority of the funding was the local authority so not sure on the relevance of the "government's Levelling Up Agenda" ? (Unless you're trying to make a cheap point).
To quote
http://www.dorsetcommunityrail.com/purbeck-community-rail-partnership/ :
"In 2010, Purbeck District Council and Dorset County Council committed £3.2million for re-signalling improvements and other work needed between Wareham Station, Worgret Junction and
Swanage Railway‘s existing signalling system at Corfe Castle. This work is part of
Network Rail‘s 2013 Poole to Wool re-signalling scheme.
BP also contributed £500,000 towards works at Norden Level Crossing. This was a legacy donation to the community when the oilfield was sold to
Perenco UK Limited
Swanage Railway was awarded a £1.47 million government grant from the Coastal Communities Fund. This successful bid helped provide the finance to enable the refurbishment of rolling stock and improvements to the infrastructure."
So the last bit was from Central Government, but was part of a wider grant package to Coastal Communities across the UK for example the "Round 5" funding from 2018 details are here:
And includes payments of £ 2.4m to Whitehaven to create a dedicated facility for water sports and recreational activities and storage facilities at Whitehaven Harbour, £ 2.1m to Forest of Dean council to develop safe, attractive transport routes into Lydney Harbour and develop the area as a recreation and tourism destination, £ 3.6m to redevelop the Old Town Hall building in Hoylake to create an arts based leisure and retail hub and £ 1.75m to Blackpool Council to create Blackpool’s first museum, which will tell the story of Blackpool’s role in the development of British popular entertainment and the Great British seaside holiday.