French Syrahs tend to be quite a lot lighter than the Australians. Even if it's possible to find a £20 Cote Rotie or Hermitage I wouldn't touch it with a shitty stick. If you do want a French bottle, a St Joseph or Cornas would probably be the best bet but I'd go to an independent wine shop and get their recommendation. Likewise a lot of New Zealand (which is quite rare) and Chilean Shiraz is cool climate so relatively light.
Of the Australian stuff, D'Arenberg Laughing Magpie is a particular favourite here – about £15 in Oddbins. It's pretty weighty but has a touch (5% maybe) of Viognier in there to soften the wine and make it slightly more mellow. Footbolt (about £11) and Lovegrass (about £10) are also good.
I've had the Shaw and Smith stuff – is good as well.
Would add Mitolo to the list of good Shiraz producers, their Jester is a bit weird but the GAM and Savitar are awesome (I think Savitar is out of budget but you might just get a bottle of GAM for £20).
EDIT: Also Charles Melton stuff