Hi I am wanting a 10 inch tablet with a hdmi output, not the type that you need to power via the charging port but one that directly plugs in, I have a budget of about £170. Any recommendations

Thanks

The Acer Iconia tab 10 is very good and has a HDMI port. At Argos, the price has gone down to £149.99 now.

Personally, I always prefer a wireless solution where possible eg using a Chromecast, partly for convenience, and partly to minimise wear and tear on physical connection ports.

I accept a wired solution is the only practical solution when time lag issues are important eg playing games.

I have a Linx 10 and it's great. Has HDMI out and unlike the iPad you can choose whether to duplicate the display on the external screen or extend instead, so you can play a HD movie on a HDTV while using the tablet to check your email or browse the net. When using it as a PC you can run it as a dual monitor display, being able to drag folders etc from one desktop to the other, as you can with any dual monitor PC. It supports all different screen resolution so you can run a HD monitor alongside the tablets own display.
This model runs Windows 8.1, full Windows 8.1, so you can install any PC software you want. The newer model runs Windows 10 but charged through a micro USB.
The W8.1 model can be upgraded free to W10 but I tried it and went back to 8.1. I love W10 on my PC but on a tablet W8.1 is far better IMHO. The swipe gestures make it far quicker and easier to use. Even installing Chrome for web browsing lets you swipe right to go back to the previous page, far easier than hitting the tiny back button. It also has a micro SD card slot so you can easily add more storage.

The new model does have two standard size USB sockets, which is nice. The older one has one micro USB. They supply an adaptor with it.

There are keyboards available, from Linx and third party but I haven't tried any so can't really comment.

Changed my budget to £250. When I stream video using miracast I get the skip every few seconds, my friend has an hudl 2 and his played video with no picture issues, I have a galaxy pro 10.1 but it has no hdmi also it 16:10 format so only played with a border all the way round so I need a 16:9 aspect ratio tablet for full screen

I don't think any tablet does true 16:9.

Miracast streaming is does depend on power of tablet to a degree, bit should not have an issue unless tablet is really underpowered or old.

Chromecast is much better when casting Chromecast friendly Apps as you can even turn tablet off.

The Linx 10 I linked to above can do 16/9. The ratio and resolution of the tablets own display is nothing to do with the external display. If you plug in a 16/9 HDTV or monitor you set the display to that setting. The settings are exactly the same as your desktop PC under display settings.
Plus of course whatever media player you choose to use can have its own settings. I use either Windows media Player, the windows Metro video app or usually Media Player Classic which has its own display settings.