TL;DR version of this post: yours is not the worst connection, but I'd still pack a spare pair of knickers in your onboard bags just in case.

Longer version: there's no priority bins for Club on short-haul (which explains why Club Europe bags often turn out anywhere but the front) due to space, but there is a terminating/connecting segregation instead. So your bags will be in the connecting bin and will be driven into an input point to be fed into the system. The good news is, as far as I can remember, domestics arrive pretty near to those so there shouldn't be too much traffic in the way.
The problem is that all bags get scanned at LHR, even if they're from a domestic inbound. So even if you don't do a security check as a passenger, your bag does and there might be hiccups. If you ever wondered why this is the case, why other countries enable tail-to-tail transfers and don't re-scan passengers on a transfer if coming from a 'secure' destination, please write to whomever is the head of the DfT this week.
Bag short-shipment at LHR is in the region of less than 1% of all bags moved in a year, but if you think that the airport moves million of bags... it still racks up to large numbers.

On a side note, I don't know what sort of six week journey you're going into, but I've once lived out of a small (40lt) duffel bag for 2 months. Sure, I worked on trail maintenance but...