Don't worry, no complication with having a checked bag at all. You can still go landside with checked bags with no issues.

In fact, if the transfer security is busy, going landside and clearing security can be faster so I do it quite often.

Availability of showers may be better (no waiting / shorter waiting time) at the Arrivals Lounge than at the lounge complex, so you may like to go there for the shower. As an arriving F passenger, you can use the Concorde Breakfast Room within the Arrivals Lounge. Concorde Breakfast Room is located behind the glass doors inside the Arrivals Lounge. As you enter the lounge from the reception, if you look straight ahead, you're looking at it.

A word of warning though. I urge you not to try to go to the Arrivals Lounge if your inbound flight to LHR is quite late, because you may miss conformance (you probably know this but 35 minutes at the boarding pass scan at security) to EDI. In this case, it's safer to stay airside.

Arrivals Lounge (including the Concorde Breakfast Room), F lounge and CCR airside serve English breakfast. If you are pressed for time, the best option is the buffet at the F lounge airside as it is the quickest and safest out of all the options as you remain airside, and self-service.