I'm not sure there should be an automatic right to appeal anything, as every disgruntled LiP will want to appeal to the UT, which would be faced with an unmanageable deluge of unarguable appeals. I'd suggest a right to appeal to the Upper Tribunal should be subject to obtaining permission to appeal, either from the lower tribunal or the UT itself.
I'm also minded to suggest there should be a small but reasonable fee (say £50 - £100) to be reimbursed by the council if the appeal is successful, just to discourage appellants from pursuing appeals just where they disagree with the adjudicator. Lastly I don't think an appeal to the UT should pause enforcement, because otherwise people will pursue UT appeals just to delay payment, rather than because they actually believe they have a meritorious appeal.
LT and the TPT handle over 200,000 appeals a year between them, if 10% were appealed to the UT that would more than double the UT's workload, and a proposal that would potentially double the UT's workload overnight (or worse) wouldn't get off the ground.
I do quite a few appeals myself, and I can think of only 2 or 3 cases in the last year which would have merited an appeal to the Upper Tribunal.