Pro-ject used to make some pretty decent decks for budget money such as the debut 1/2, they weren't as good as a Rega but only cost about £120 with a cartridge, ready to go. Pro-ject sadly have pushed the price right up on the newer debut decks, they are improved but not such good value at £300-350!
The current budget models such as the elemental and essential look very cheap and nasty to me.
The best bang for buck new deck for me is the Rega RP1, not much more than an elemental and about the same price as the essential and better than both in just about every respect, in fact I'd argue that it's better than the debut carbon.
If £160 is the absolute maximum you can spend I'd be patient and wait for a good used deck, a Rega P2 is always a safe bet and should be achievable for less than £160 if you're patient.
Another budget-ish favourite of mine is the systemdek iix, they are lovely decks that sell for bargain prices considering what they are but you might struggle to find one within budget. It's still worth keeping your eyes open as I have seen them go with a Rega RB250 or linn basik arm for below £150, the arms alone sell for that but sometimes when fitted to the deck are not mentioned in the listing title and don't attract attention, so you get the whole shebang cheap.
The same goes for the manticore mantra as the systemdek.
I'm not so familiar with the technics linear trackers mentioned by Avole but did notice some at beer money prices when browsing for ideas earlier, they look interesting considering the prices.