Interleaving is certainly an issue, typically adding 8ms to ping times. FTTC interleaving will be the same regardless of which SIP.
My latency was poor on BT because of very poor internal routing in the BT internal network (Winchester->Sheffield->London) that typically added another 9ms to pings; around 22ms to bbc without interleaving. This has been much better on Plusnet, around 13ms without interleaving. I suspect that difference will vary a lot depending on where you live; many people quoted sub 10ms pings on BT.
Recently moved from BT Infinity 2 to PlusNet. Very happy so far.