is the thermostat very close to the 2860? or taking from the same electric socket power? can you try to connect one or the other to an other electric socket?

The thermostat is powered from the boiler not a mains outlet. The router and the thermostat are in different rooms. WLAN signal strength shows on the thermostat as 75%. With WAN2 only enabled the thermostat functions perfectly so I do not think the wireless connection between router and thermostat is the problem I think it is something else?

Thanks for your comments.

Regarding the admin post about packet capture can you point me in the direction of instructions of how to do this please? I cannot lend out my thermostat as it is hard-wired to boiler so not removable by end user.

Thanks.

In mean time till you get packet capture, can you try the modem to set the wifi to G or N only & see if any change? Wireless LAN >> General Setup>Mode
also try (if you didn't) some combination to change wifi settings at Wireless LAN >> Advanced Setting
You can also try to turn the antennas of the modem to different direction so it means the other wifi meter could pick up less signal from the 2860

EDIT
if when using the wan 1 and is not working the netstat wifi it makes me think the phone line may pass near by the boiler
I know other cases where even car alarms affected from wifi

Thanks for the email.

Pretty certain it is not a wifi problem since Nest connects fine when I use WAN2 only. Wifi also connects if WAN1 is enabled but their is no internet connectivity. I have tried the suggestion but no change I an afraid.

Pretty certain it is not a WAN1 (BT Broadband) or wiring problem since Nest works fine with BT Home Hub.

Very much leads me to think that something needs configuring that I am missing.

Very frustrated!

ok maybe i miss understood
we know when you connect the BT modem (not the 2860 at this point) everything works normal (perhaps the thermostat was set for that modem)

1-when you use wan 1 (direct the 2860 modem to the phone socket) is internet (line)working normal? can you browse web pages?
If yes until now ... does wifi works normal for your smart phone? or any other device such laptop?

2- according to the video below (assuming i got the right product) it say you can control the thermostat via smartphone only, have you checked with your smartphone if needs any settings for the new modem connection (2860) such at 0:55 maybe the new password for the 2860?
http://support.nest.com/#install-your-protect
so what i mean connect the phone to the wifi network of the 2860 & then from the thermostat apllication get the wifi of the 2860 and set it again for this modem##am i correct?