Those ping scores and the timing certainly would point to a utilisation issue. I've taken a look at the area stats and the utilisation certainly gets worse at those times. At present it's not quite breached thresholds to be raised to networks but it is very close so I've asked for this to be monitored and raised as soon as possible.
Really sorry that you've had problems with peak time broadband speeds, though I can at least let you know that thresholds have most definitely been breached.
I've just escalated this over to Networks and shall provide you with a fault reference number as soon as they get back to me.
I've noted full details of this on your account and would advise you to call in (each month) to request a credit, until the forthcomng network upgrade has been completed (just dial 150 - free from a VM landline or 0345 454 1111).
This type of network upgrade can take months to plan and implement, though a lot of this type of work is being done post-christmas so hopefully you shouldn't have to wait too long. But do please request updates on here and we'll check for progress for you.
My tests of your connection also revealed a low modem SNR which will also impact on speeds and general broadband performance. So I'd like to arrange for an engineer to visit to get this sorted out for you.
I'll send you a PM in a moment (small red envelope icon, top left of page) and shall schedule an appointment as soon as I recieve your reply.
I've just checked on F003346711 for you and the upgrade work is still in it's planning stages at the moment. A review is due at the end of December, at which time we should have some more information for you.
Sorry, as I know this is probably not what you wanted to hear, but do at least make sure you call in for your credit each month.
The upgrade work itself can involve: implementation of additional upstream and/or downstream channels, hardware upgrades at the CMTS, re-siting of street cabinets, digging up of roads/paths etc.
Most of the time planning permissions have to obtained from the local authority for some of this work. Plus, the extra drain on power has to be calculated and presented to the supplier. All of this combined does, sadly, take some time and that's without calculating finances and engineer availability.
This is why you are able to request credit whilst this is ongoing (instead of waiting for it to be actually fixed, as you would with other faults).