Poor connection and speed - new ideas please!

Question

I'm hoping that someone might have an idea that hasn't already been suggested - I'm desperate.
Bear with me while I explain the issue as a lot of it was actually with Sky (but is recurring with BT).
I moved into a new house in February this year and had a phone/broadband connection with Sky.  At no point since then were they able to get me a stable connection or reasonable speeds.  Connection also drops if the phone is used.
Promised between 1-3mbps actually got on average between 0.15 and .80 mbps. 
During countless calls to their technical services they'd tweak settings and adjust this and that and occasionally the speed would go up over 1mbps only to drop off within a day. 
Sky sent new microfilters and even a new router.  They also sent a BT Broadband engineer to test the voice line - he said everything was fine although the phone line was crackley.
After months of this I spoke to BT sales who said (when I specifically asked why they'd be better than BT and how do I know the problem won't just recurr with them) that their router was the best in the business and that anyway I'd be able to buy the accelerator to enhance speeds whatever they turned out to be. 
So I signed up with BT and cancelled Sky.  BT broadband and phone were connected on Thursday this week.
I was overjoyed on Thursday to see a connection speed 1.7mbps (it's so sad that that's a good speed for me!) but this quickly dropped off.  Turns out I can't install the accelerator as I have the wrong type of socket.
Yesterday the speeds were around 160kbps (I'm aware that it might take a few days to stabilise).  The connection itself has been much worse than Sky.  It was off ALL of yesterday apart from a hour or so in the morning.  It was off this morning from 6am to about 10 minutes ago. 
So that's the background. 
Basically I've had new microfilters, new routers, new phone, new wires (ethernet and phone), engineers checking the BT voice line, changes of wireless channel, moving router to different sockets, unplugging the phone entirely, unplugging the TP wireless connector for Sky Anytime +. 
Pretty much - you name it I've done it. 
I haven't yet contacted BT engineers.  Soon as I pick up the phone the internet connection will drop (same reason I haven't yet tried the quiet phone line test).  I'll do it later once I posted this message in the hope that someone out there will have a different idea of what might be going on.
Important note - my house is brand new.  It doesn't have the normal master socket / test socket setup.  It has a grey external test socket.  All interior sockets are plain single piece sockets.  I've had the covers off all of them to confirm.
My neighbours are having similar problems.  Assuming that the BT engineers are right and that there's nothing wrong with the line to the house(s) and nothing wrong with the equipment within the house (big coincidence that both Sky AND BT's stuff would be broken) I'm left with the only possible other bit - the lines/sockets between where the BT line enters the house and the equipment. 
Is it feasible that this could have been installed incorrectly?  How would I check?
Any suggestions welcomed (as long as it's not changing microfilters - I could open a microfilter shop I have so many).
Thank you for bearing with me - I really appreciate it.
Stats:
Connection Information
Line state:
Connected
Connection time:
0 days, 01:11:12
Downstream:
160 Kbps
Upstream:
448 Kbps
ADSL Settings
VPI/VCI:
0/38
Type:
PPPoA
Modulation:
G.992.1 Annex A
Latency type:
Interleaved
Noise margin (Down/Up):
8.4 dB / 15.0 dB
Line attenuation (Down/Up):
64.2 dB / 31.5 dB
Output power (Down/Up):
13.8 dBm / 12.6 dBm
FEC Events (Down/Up):
3270 / 8
CRC Events (Down/Up):
5 / 0
Loss of Framing (Local/Remote):
0 / 0
Loss of Signal (Local/Remote):
0 / 0
Loss of Power (Local/Remote):
0 / 0
HEC Events (Down/Up):
4 / 0
Error Seconds (Local/Remote):
1 / 0

Answer 1

Hi - thanks for the replies.  Sorry for not responding sooner - broadband has just come back on.
Unfortunately before I read your reply I contacted BT helpdesk (India) and told them the whole story...  They did a line test and said they were escalating it to the exchange engineers and they'll be calling me back tomorrow - so we'll see.
From what you've said it sounds like I need to concentrate on getting the phone line fixed first (I rarely use it so haven't been that bothered).  I read somewhere else that a similar problem might have been caused from the cabinet - corrosion in the connections etc. no idea if that applies to my case but at least it's another angle.
The connection is coming and going at the moment - couple of minutes on and then off again for a while.   
Thanks again for your suggestions.