Hi Geoff.  Long time no see.

First, create this function.  It's a "programmable" Tally function.


 CREATE FUNCTION [dbo].[fnTallyProg]
/**********************************************************************************************************************
 Purpose:
 Given a start value, end value, and increment, create a sequencial list of integers.

 Programmers Notes:
 1. The increment can be negative if the start value is greater than the end value.

 Revison History:
 Rev 00 - 18 Feb 2017 - Jeff Moden
        - Initial creation and unit test.
**********************************************************************************************************************/

        (
         @pStart     BIGINT
        ,@pEnd       BIGINT
        ,@pIncrement BIGINT
        )
RETURNS TABLE WITH SCHEMABINDING AS
 RETURN WITH
 E01(N) AS (SELECT 1 FROM (VALUES (1),(1),(1),(1),(1),(1),(1),(1),(1),(1))E0(N))    --10 rows
,E04(N) AS (SELECT 1 FROM E01 a CROSS JOIN E01 b CROSS JOIN E01 c CROSS JOIN E01 d) --10 Thousand rows
,E16(N) AS (SELECT 1 FROM E04 a CROSS JOIN E04 b CROSS JOIN E04 c CROSS JOIN E04 d) --10 Quadrillion rows, which is crazy
            SELECT TOP (ABS((@pEnd-@pStart+@pIncrement)/@pIncrement))
                   N = (ROW_NUMBER() OVER (ORDER BY (SELECT NULL))-1)*@pIncrement+@pStart
              FROM E16
             WHERE (@pStart<=@pEnd AND @pIncrement > 0)
                OR (@pStart>=@pEnd AND @pIncrement < 0)
;
GO

After that and using your good test data, the problem becomes trivial.


 SELECT  t.Id
        ,Continuous = s.N
   FROM #T t
  CROSS APPLY dbo.fnTallyProg(t.StartSeqNo,t.EndSeqNo,1) s
;