You have 28 days to submit to POPLA so let's work on it a little. With POPLA, you have one chance to submit your case and once its submitted, no further evidence may be submitted. I'd also wait until you hear back from the gym managers before submitting. If the operator put someone to work on creating an evidence rebuttal package, they're going to use the fact that they've put money into the proccess to attempt to recover the invoice they've issued - lets not hand them to much ammunition.
That being said, lets go point by point;
Your Introduction
I'd keep the first two sentences. Bin the rest of it. These companies are not known for their use of discretion - they're whole bussiness comes from people paying their invoices! If you hand to them evidence that you knew the proccess, they're going to use it.
1. No Evidence of Landowner Authority
Yep, fair enough. Be prepared for them to supply the contract when they provide their evidence.
2. Inadequate Signage – BPA Code of Practice Breach
I'd take out the bit where you admit to knowing the process for the reasons I've already outlined. I've had a look on google street view and there does appear to be a sign at the entrance, however, it appears it can only be seen if you enter the car park traveling northbound on Maidstone Rd - bare in mind, I'm going on images from 09/24, If you could supply photos of up to date signage with timestamps (using an app such as timemark) this may assist us and your case.
You could add a quote from the BPA code of practice - Clearly a breach if you can only see from one direction.
The size and positioning of the sign must take into account the expected speed and direction of travel of vehicles approaching the entrance and must be visible
(i.e. not be obscured e.g. by foliage or other objects).
3. No Grace Period Applied – BPA Code of Practice Clause 13
I'm not sure this is relevant really. Generally by grace period, they mean 10 mins. This is to come in and decide if you want to accept the terms.
4. The Charge is Not a Genuine Pre-Estimate of Loss and Is a Penalty
They'll attempt to rebutt this but I don't think it's harmful to keep it in
5. I Was a Legitimate, Paying Customer
Again, I think it'd be better to remove traces that you're aware of the process.
6. CEL’s Evidence Must Be Scrutinised for Accuracy and Timeliness
I'm not sure if this is relevant. This is how POPLA works. The operator sees your evidence and responds with theirs. Even though the the assesors are supposed to be independent, I wouldn't want to taint their view of the case.
This is only how I see it and I welcome anyone else to put their opinion forward.