Chasing them up isn't probably going to have any effect.
And there's no "standard" time - because the number of claims will have been steadily mounting over the last few weeks, with no corresponding increase in manpower to review the claims, it's only to be expected that turnaround times are increasing. I'd advise a little patience.
The more detail added, and the more attachments enclosed (so: the more receipts included for reimbursement) the longer it will take to process.
If it's a straightforward compensation claim only, then it shouldn't take long (my last claim, almost exactly a year ago and in a period when there was no such disruption, and which was a simple claim for compensation with no duty-of-care claims, took 12 business days to reach a positive outcome). Anything that involves duty-of-care expenses will take longer.