Her birth index:

First name(s)         ELIZABETH R
Last name             FOWLER
Birth year            1925
Birth quarter         4
Mother's maiden name  Rutherford
District              Cambridge
County                Cambridgeshire
Country               England
Volume                3B
Page                  597
Record set            England & Wales Births 1837-2006
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No death or other entry found under the name of Taylor.
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There are 61 Taylor births with a mother’s maiden name of Fowler.  This is far too many to even hope to identify any children she might have had.  It will probably take until the 2051 census to hope to access any births up to 1951 and probably will need the 1961 census as well.  I shall be well under 6 ft below by then.
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There is birth for Kitty Ruth Taylor, her father’s co-executor:

Year  Surname  Forenames  District
1958  Taylor   Kitty R    St Albans, Herts

From the internet there are two further daughters whose married names are Harriet Rutherford Smith and Susan Elizabeth Moss.  There birth indices are:

Year  Surname  Forenames  District
1952  Taylor   Harriet R  Macclesfield, Cheshire
1962  Taylor   Susan E    St Albans, Herts

So Elizabeth and Henry could have started off their married life in Cheshire, then moved to St Albans and retired to the lake district.  A search with these locations brings in:

Year  Surname  Forenames  District
1953  Taylor   Jane C     Macclesfield, Cheshire
1956  Taylor   Polly F    St Albans, Herts
1964  Taylor   Henry R    St Albans, Herts

Nowhere is there any mention that they had a son, let alone one named Henry, though it does sound possible that he might have had one with the same name as his.  If Henry is removed, the above leaves five daughters which is what can be found in some internet gossip site.  Try the electoral rolls?
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Their church wedding:

First name(s)                   ELIZABETH RUTHERFORD
Last name                       FOWLER
Birth year                      1926
Marriage year                   1949
Marriage day                    20
Marriage month                  Aug
Spouse's first name(s)          HENRY SHEARER
Spouse's last name              TAYLOR
Place                           TRUMPINGTON
Groom's first name(s)           Henry Shearer
Groom's last name               TAYLOR
Groom's marital status          bac
Groom's age                     28
Groom's occupation              schoolmaster
Groom's residence               of 1 Oaklands Avenue Gosforth
Groom's father's first name(s)  Ernest Miens
Groom's father's occupation     estate agent
Bride's first name(s)           Elizabeth Rutherford
Bride's last name               FOWLER
Bride's marital status          sp
Bride's age                     23
Bride's occupation              student
Bride's residence               of Cromwell House Trumpington
Bride's father's first name(s)  Ralph Howard
Bride's father's occupation     university professor (deceased)
By licence or banns             by banns
County                          Cambridgeshire
Country                         England
Record set                      Cambridgeshire Marriages
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And their civil index is:

First name(s)       ELIZABETH R
Last name           FOWLER
Marriage quarter    3
Marriage year       1949
MarriageFinder      ELIZABETH R FOWLER married one of these people
                    Henry Y Taylor
Spouse's last name  Taylor
District            Cambridge
County              Cambridgeshire
Country             England
Volume              4A
Page number         741
Record set          England & Wales Marriages 1837-2005
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