Faulty lamda sensor Aeh/alk 1.6 sr 1999

For some time I've had this issue however when this winter kicked in its gotten worse. Starting the car  it's running rich, unsteady idle, there is a lack or delayed response. I ve posted about this before however now think there is a solution.

First of all started by cleaning the Maf, no difference, Throttle body was spotless, part of the problem as well was the theremostat was lazy it wouldn't warm up so had this changed, car mow sticks to 90c dead on. 

Got the car scanned lamda sensor came up faulty, however ever the thing is jammed in the manifold/welded in as its the original. Garage now has to spend have a day's labour as it needs to be removed out if the car or treated with heat, really hoping this will sort it.. 

Having invested after this almost 2k In replacing bits over the last year, I know now I'd be silly to move it on, but this has been on ongoing problem, I thought I'd be able to live with the rough idle however it needs to be addressed for emmisions. 

Hoping I'm doing the right thing, the car otherwise is in good shape  bodywork is clean apart from.surface rust which has been treated,

Quick question on the v5 says the engine is a Aeh, however on the scan it says ALK. I cannot find the stamp or I'd on the engine to check iam not convinced is on its original engine? Any other way to check? Have no paperwork to say the engine was swapped.

Car has 100k on it.. there is a nagging feeling that I want to move her on but the investment is telling me otherwise