How was Warwick related to the Woodvilles?

Does anyone know how Warwick was related to the Woodvilles/Wydevilles? Until a couple of days ago I'd have said he wasn't - simple. But then I noticed in Richard III A Medieval Kingship (ed. John Gillingham) the following useful analysis of Anne Neville's arms - which of course were the same as her sister's.

The following families are represented:

1. Sir Guy (This is Guy of Warwick, not Guy of Gisburn.)
2. Rohand (No idea)
3. Gwayr (No idea)
4. Newburgh (Ancestors of the Beauchamps, think.)
5. FitzPiers (Sound like a Norman family but can't say I've heard of them.)
6. Thony (Sometimes spelt TONY or TOENI. Quite famous earlier on I think. [edit] Stephen Lark tells me they were the Staffords, before the Staffords became the Staffords if you see what I mean.)
7. Beauchamp (Famous as earls of Warwick)
8. Colobrand's Head (Colobrand? Sounds like a drink.)
9. Fitzjohn
1o. Mauduit
11. Abitot
12. Waltheof (Definitely heard of him. Saxon hero married to Judith, right?)
13. Montagu (Salisbury bunch)
14. Monthermas. (Sounds like a festival of the church. Do they mean Monthemer? Or whatever the guy was called who got off with Joan of Acre.)
15. Neville (Well yes, we certainly know about them.)
16. Beauchamp (ancient) - bit repetitive, but I suppose it emphasises the Beauchamps.
17. Aeneas (The Greek guy? He had a coat of arms? Cooool!)
18. Balliol (As in Scotland. Probably via the Despensers if I recall aright.)
19. Eldol
20. FitzHamon (Definitely via the Despensers)
21. Consul (As above)
22. Clare (Yep, Despensers again, though probably by other routes too. Those Clares got about)
23. Burghersh. (Despenser lot again. Thomas D's mother, actually.)
24. WYDEVILLE - which is the posh way of spelling 'Woodville.' How did they get in among this lot?
25. Despenser (Obviously)
26. Weyland (Another Despenser input.)

So now we know what Anne did with her youth - embroidering that little lot onto all the cushion covers must have taken hours. You know dear a family tree program would have been much more useful...

But seriously, does anyone know how the Wydeville/Woodville family were related to Warwick? Because it looks as if they must have been.

Founders and Benefactors Book of Tewkesbury Abbey

This book, which belongs to the Bodleian Library, is online here and some of you may be interested. It includes portraits of the various patrons of Tewkesbury Abbey including Robert Consul, Gilbert de Clare, Hugh Despenser the younger, Thomas Despenser, Isabelle Despenser (she actually gets two illustrations!), Richard Beauchamp, Earl of Warwick, Warwick the Kingmaker and George Clarence.

The work dates from early Tudor times and the costumes depicted reflect this, but the extensive heraldry is well worth careful study. For example on Thomas Despenser's page you will find his marital impalement with Constance of York ** and also an illustration of the short-lived impalement of Edward the Confessor's arms with the royal arms used by Richard II from circa 1397-99 as a mark of his devotion to the Saint.

**At least that's what I take it to be - the one that Thomas is more or less pointing at with his right hand. But oddly, the artist has placed Constance's arms at heraldic right (the left as we look at it) and Despenser's at heraldic left. Which is the wrong way round. Theoretically this coat represents a marriage between Edmund of Langley or Edward of York and one of Thomas's sisters! You see, you can't even trust prime manuscript sources completely.