If you getting working normal the adsl after used the TT one ... to me seems like it may need different modem code or change filter at socket ... perhaps phone cable ... you can also try with out filter just with a splitter like this
http://www.lankalaptophouse.com/image.php?type=P&id=17972

What Modulation do you think we should us?

I've updated the Firmware.
Plus I have change the routers MAC address to make it the same as the TT one.
I know this can help from trying to get a Cisco2911 on to sky BB

I have added that type of filter too

when i was with TT they used adsl2+, because seems you are far from the exchange you can try change the modulation manually to adsl2 (not plus) if helps in combination with an other filter, if i remember i had a d link filter from the box of an old TT supplied d link 2680
ADSL Nation XF-1e Professional Microfilter has good rep but never used with a 2860 / 2760

That type of filter (only splitter) use it alone (if will make any difference) with out any other filter connected

Because of the line length the line has been modified down from ADSL2+

Should I leave DSL modem codes? Should I leave them as default?

If TT has change the modulation maybe that is why the modem only locking with G.dmt
Also the real attenuation for your line i believe should be 58 (52 reporting with g.dmt) - based on this article

Because the router measures against the frequencies available, some users may notice a very slight increase in attenuation if say moving from a fixed rate 512 kb connection up to 2Mb.
Higher frequencies such as those used to transmit faster speeds are more likely to be attenuated (higher frequencies = higher attenuation).
ADSL 2+ has an increased frequency spectrum, therefore an increased attenuation of around 3-4dB is not unusual.

http://www.kitz.co.uk/adsl/linestats.htm#attenuation

If you know to use this toll (just add the 58 for atuenuator, speed 3800 you getting and snr 9)
http://www.coolwebhome.co.uk/calc/index.php
Then you will see that the 2860 is getting more speed than the calculator, which means the 2860 is working really good with the TT line because you synchronize just over 3.800 kbps, so i don't think is modem issue

personal i think you need either a good filter or modem codes will help little better to be more stable
The modem codes are limited at the moment with the 2860 (only 2, compare to 2830/2850 which are about 10 to choose ) & can be find at wan > general setup > dsl modem codes & can swap to see if one is better (stable) than the other

You can also ask TT to set your snr target at 12 db ( from the stats at your first post is 9), that will help the line stay stable and i think this seems the best option
:arrow: Note if you have other phone extensions may be more complicate & they should help you better in there because they can monitor your line
When i was with TT the forum support was way better than the phone support
At TT forums the OCE are very good for helping so ask to increase your snr value

EDIT
other advise is to check if you have any bad cabling at home (broken somewhere or moisture inside the phone socket) and also if you have the 2860 near by any other electrical device try move it away if is better ... or long cable over 2 meters from the phone socket to to modem, make it shorter because in that long line you have may affecting connection

I have two choices: adsl2 (g.9923) and ADSL2 annex m/j
Switch on is best?