LE3 doesn't have just one uBR it's covered by at least 2, one legacy and one overlay network.
The legacy CMTS, there will be more than one of these feeding LE3, is good for 2,400 connections depending on loading levels, 300 customers per 38Mbps downstream seems reasonable.
The Cisco 10k is good for tens of thousands. It has 8 line card slots each of which can support 20 downstreams and 20 upstreams, or it can feed an external modulator.
There are 15 CMTS in Leicester hubsite, another 13 in Northfields, LE7, at least 2 of which in each site are 10k or BSR.
I'm confused by the statement about 2000 users being a 1.2% take up though.
LE3 LEICESTER Braunstone, Glenfield, New Parks, Groby Road (A50), Leicester Forest East, Westcotes
I doubt that that area is a population of 200,000 given that the city's population is listed as 300,000 and remembering that a 'user' for cable purposes is a cable modem, and there's only one allowed per property. Even at 100% take up there would not be 200,000 cable modems in the whole of Leicester, the average home having over 2 residents per premise.
Braunstone apparently has about 7,500 households, Glenfield 5,000, New Parks 8,000, Westcotes 4,000, unsure about the other two and can't be bothered to search that hard but nonetheless it's not 2,000 households, 26,000 + those two areas so at 60% takeup a next generation CMTS plus a couple of legacy ones would be fine!
Your issues stem from a lack of 16QAM upstreams and the DOCSIS 2 upgrades, once all that's done along with the ongoing resegmentation that's being done for downstream and network quality purposes your upstream capacity issues will be gone with no need for any further additional upstream ports.
He says optimistically.
TLDR - the amount of chassis are fine.