This is a list from a GI Bill search of approved schools in the UK. Do any of these offer research (dissertation only) PhD or ThD in Theology? ANGLIA RUSKIN UNIVERSITY ANGLO-EUROPEAN COLLEGE OF CHIROPRACTIC BANGOR UNIVERSITY BATH SPA UNIVERSITY BIRKBECK COLLEGE, UNIVERSITY OF LONDON BLACKPOOL AND THE FLYDE COLLEGE BOURNEMOUTH UNIVERSITY BRITISH SCHOOL OF OSTEOPATHY BRUNEL UNIVERSITY CANTERBURY CHRIST CHURCH UNIVERSITY CARDIFF UNIVERSITY CHELTENHAM & GLOUCESTERSHIRE COLLEGE OF HIGHER EDUCATION CITY UNIVERSITY LONDON COVENTRY UNIVERSITY CRANFIELD UNIVERSITY CUMBRIA INSTITUTE OF THE ARTS DE MONTFORT UNIVERSITY FALMOUTH COLLEGE OF ARTS FARNBOROUGH COLLEGE OF TECHNOLOGY GOLDSMITHS COLLEGE, UNIVERSITY OF LONDON HARROW COLLEGE OF HIGHER EDUCATION HOMEOPATHIC COLLEGE OF EAST ANGLIA HULL COLLEGE HULT INTERNATIONAL BUSINESS SCHOOL HURON UNIVERSITY USA IN LONDON IMPERIAL COLLEGE LONDON KEELE UNIVERSITY KEELE UNIVERSITY KIDDERMINSTER COLLEGE KING ALFRED'S COLLEGE KING'S COLLEGE LONDON KINGSTON UNIVERSITY LANCASTER UNIVERSITY LEEDS METROPOLITAN UNIVERSITY LEICESTER WARWICK MEDICAL SCHOOL LIVERPOOL HOPE UNIVERSITY LIVERPOOL JOHN MOORES UNIVERSITY LONDON ACADEMY OF MUSIC & DRAMATIC ART LONDON BUSINESS SCHOOL (UNIVERSITY OF LONDON) LONDON COLL OF TRADITIONAL ACUPUNCTURE & ORIENTAL MEDICINE* LONDON FILM SCHOOL LONDON METROPOLITAN UNIVERSITY LONDON SCHOOL OF ECONOMICS LONDON SCHOOL OF HYGIENE & TROPICAL MEDICINE (UNIVERSITY OF LONDON) LONDON SCHOOL OF OSTEOPATHY LONDON SOUTH BANK UNIVERSITY LOUGHBOROUGH UNIVERSITY MANCHESTER METROPOLITAN UNIVERSITY MATTERSEY HALL MCTIMONEY COLLEGE OF CHIROPRACTIC
Unless something has changed since 2009, when I discussed the issue of GI Bill approval for study at non-US universities by distance learning with the University of Leicester in the UK, the VA won't approve it, although they will approve B&M attendance at schools that have been approved.
In addition, just because the degree is "dissertation only" does not mean it is necessarily a "distance" PhD. Most would expect the student to be physically there, doing the research, assisting with teaching, and other duties. One of my friends did a "dissertation only" PhD in the UK, and lived an hour away from campus. His adviser would not allow him to do to any work from home because his desk and chair was not approved by the university's ergonomic standards.
UK docs Like others, I seriously looked into the UK doctoral option, but with the at least once per year on campus requirement, discovered it would cost nearly as much as a US doctorate [travel, a big cost]. A good friend of mine went the UK doc route. The travel and costs about wore him out.