There's a useful list of SSW events up to 2014 that were identified as major included in this paper:

https://www.earth-syst-sci-data.net/9/63/2017/essd-9-63-2017.pdf

The paper, entitled "A sudden stratospheric warming compendium", appeared in the journal Earth System Science Data, issue 9 in 2017. It was written by Amy H. Butler, Jeremiah P. Sjoberg, Dian J. Seidel and Karen H. Rosenlof. From it, I have extracted the central dates of major Northern Hemisphere SSWs detected by at least 3 out of the 5 or 6 available reanalysis products between 1979 and 2014:

22-Feb-79
29-Feb-80
4-Mar-81
4-Dec-81
24-Feb-84
1-Jan-85
23-Jan-87
8-Dec-87
14-Mar-88
21-Feb-89
15-Dec-98
26-Feb-99
20-Mar-00
11-Feb-01
31-Dec-01
18-Jan-03
5-Jan-04
21-Jan-06
24-Feb-07
22-Feb-08
24-Jan-09
9-Feb-10
24-Mar-10
06-Jan-13

Instances by month: Dec 4, Jan 7, Feb 9, Mar 4

Note the gap of over 9 years between Feb 89 and Dec 98 when there were no major SSWs detected.

Going by those dates, the great majority of the coldest UK winter months were not preceded by a major SSW. The cold December of 1981 and cold spell of January 1982 were, as were the cold Jan and Feb of 1985, the cold spell of early February 2009, and arguably the cold March of 2013 (though there's rather a long delay). But the winter of 1978-9, Feb 1986, the very cold spell in Jan 1987, the winters of 1995-6 and 2009-10, and Dec 2010 were not. As the data used only goes up to 2014, the SSW of last February is not included in the table.

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Its not as straight forward as that
you need to review those into PV displacement & split events -

Then where the lobes of the PV & went after the split / Displacement -

The biggest correlator post SSW events is the mode of the AO

Its not as straight forward as that
you need to review those into PV displacement & split events -

Then where the lobes of the PV & went after the split / Displacement -

The biggest correlator post SSW events is the mode of the AO

I'm sure you're right, and no doubt those factors might explain why some of the major SSWs were followed by severe UK weather while others weren't. But more detailed analysis will have to be done by someone with a lot more knowledge than I have. At least the list of SSWs that have been identified as "major" by the authors of that paper could provide instances worth examining in more detail.

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