No Network Rail HAS to do the work if a Toc asks and it cant charge them for it, say you have a line with four car long platforms and a toc says it wants to run 6 car trains then NR HAS to lengthen all the platforms and cant charge them for the work as its part of their service obligations. The funding comes from their 5 year settlements from Government as part of regular maintenence requirements. If they wanted upgrades in station facilities like ticket office, platform shelters, etc.. then the Toc has to find the money itself.
In the seperation of funding and maintenence responsibility to trackside and station side platform length is considered a trackside improvement.
It's very little to do with what the TOC wants, requests or needs. NR will only do the work if DfT specifies it and provides the funding. At the same time the DfT will (usually) also specify amendments to the franchise requiring The TOC to provide longer trains. There are exceptions, the Tilbury loop being case in point.
The other, much rarer option is if a TOC or third party enters into a contract with NR; Essex CC, BAA, WYPTE have all done this recently.
Anyway, back to the original point, the problem platform on the T&H is at South Tottenham.