How will this affect ones such as North East Lincs Council who run the 55 in Scunthorpe?
Not sure.
Do we know what basis NE Lincs have done this? There are circumstances where a local education authority (which NE Lincs, as a unitary council is) can use its buses to provide local bus services, and certainly at one time they were exempt from some elements of operator licensing in doing so. Lincs CC had its own Translinc operation which ran a number of local bus services - it was later privatised.
Kent County Council also had 'Kent Top Travel' at one time in the not so distant past.
Could someone explain the difference between a tendered service and a franchise please?
Broadly speaking, a 'tendered service' outside London at the moment is a bus service (could be anything from a single journey to a comprehensive service) which the commercial market does not provide (or is about to cease to provide) which the local transport authority considers 'socially necessary'.
The council procures the service from a bus operator by inviting tenders to operate in accordance with a specification. That tender becomes the price the council pays the operator to run it. (For something relatively small scale, councils can do it without a formal tender)
Exactly how it works varies - councils can set the fares and (in effect) keep the revenue, the operator getting a fixed price to operate the service; or the operator can get a fixed subsidy but also keep the revenue (arguably giving the operator an incentive to market and develop the service) or you can have revenue sharing deals in varying levels of complexity.
A tendered service is not immune from competition (in theory, if nobody has considered the service commercial on its own, they are unlikely to decide to take a commercial chance competing with an operator who already needs a subsidy to run it, but it has happened.)
Councils have a legal duty 'not to inhibit competition' which is a bit fuzzy but is generally held to mean that they shouldn't go out to tender for something that will abstract passengers from commercial services.
What happens in London is that TfL plan the entire network, and tender each route as a franchise. TfL keep the revenue and the operator has no involvement in marketing or pricing or anything. Once an operator has the contract to run (say) route 11, they have got that route for 5 - 7 years and nobody else can come along and compete with them. (The way the TfL contract model works, operators get financial bonus / penalty for exceeding or failing to meet various performance targets, and in theory can have contracts withdrawn for serious poor operation - this hasn't happened often.)
There is of course a tendering process in the TfL model. Both forms of tendering can (and certainly in London do) include 'quality' aspects rather than just the 'cheapest is best' approach that tended to be taken both inside and outside London in the mid 80s.
What's being proposed outside London is some form of franchising. It's a bit early to say whether councils would go for one franchise for a large area, multiple franchises for bundles of routes, or each route as a separate franchise, or what.