It's easy for folk to pick holes in a quote while sitting in the comfort of their living room. As the person asking, you've no idea whether the respondents are in any way qualified or what their motivation might be.
As it stands we've only got a vague idea of what the job might entail, and no idea what quality of gear is being proposed, nor the amount of actual work involved to complete it. For example, if changing all the cable means lifting a loft floor and removing the existing wiring internal and external of the house then £350 might be cheap. On the other hand, if you live in a strong signal area and the quote is just the aerial, amp and magic eye run then £350 feels quite top heavy. There are just too many unknowns to give a simple Yes/No answer.
The best way to approach this then is to look at the justification for each part, and to make some recommendations about the sort of quality of gear that should be used. After all, if you're going to pay for someone to change all the wiring (and there are some good reasons why you might want to do that) then you want to make sure that you won't have to spend good money after bad because the installer put in some rubbish
Bracket: Reasons to change include the bracket being very badly rusted or too small for the job. This last point is most important. I've done jobs where a previous installer put in the cheapest chimney bracket -
a 6" pressed steel - to save £4-£5 but it hasn't been able to cope with the wind loading on the aerial. These brackets are bad. Don't be talked in to one. The bracket moves and it levers the bricks loose on the chimney. It wrecks the pointing and starts a leak in to the roof space. The home owner then needs a roofer out to repoint the chimney. A fiver saved costs £300-£1000 in remedial work depending on the severity of damage and whether scaffolding is needed.
If it's a chimney and the pole is 2-3m long then an
8" mitre cradle made from galvanised steel should do the trick. If the homes around you have 20ft/7m poles because of trees or some other obstruction then you'll need either a 13.5" mitre cradle or a pair of double brackets to spread the load. Go for galvanised rather than painted steel. They last longer and look tidier.
Mast: Reasons to change include cosmetic ( it was steel and is now rusty as hell ) or to do with size i.e. it's too thin or not long enough for the job. Go with aluminium rather than steel - they last longer and don't rust. The diameter and length depend on the requirements of the job. Shorter poles (2m) should be 1.25" diameter. See
here for a general guide
Aerial: Reason to change include that it was a cheap contract aerial with poor gain, or is a grouped aerial or a high-gain wideband aerial that was good for the frequency range before the switch to digital but post-DSO the frequencies were moved and now it isn't such a good match, the aerial has fallen to bits, it's letting in water to the coax cable. [Note; there are no 'digital' TV aerials, nor are there special aerials for HD. I've done jobs where a decent
20-year-old Yagi has pulled in respectable signal levels for digital TV including the HD channels.]
The local knowledge of a decent honest aerial installer is gold. Aerials can either be broad spectrum such as the Group T Log Periodics (ch 21-60), or they can be focused on a narrower band of frequencies; for example Group A Yagi (ch21-37). The narrow focus aerials produce a stronger signal in their optimum band, so if this happens to match your local transmitter then you'll need less (or no) amplification of the signal, and that's good because it means less added signal noise from electronic amps. A good installer will know this, and also which local transmitter best serves your area.
Aerials to avoid are the now defunct wide-band high-gain types because they don't filter above ch60 where there is 4G interference for some areas of the country. There are also lots of cheap (and some not-so-cheap) wide-band high-gain aerials that are poorly made and don't last that long before bits stop dropping off. Here are some examples:
one two three
Amplification: Reasons to change include the need for more outputs, or changing to a type that will pass the Sky Eye signals. Amplification also covers masthead amps. These are an amplifier fitted very close to the aerial and used for the purpose of increasing the signal power level where reception is marginal. Being fitted on the aerial mast itself means the amp gets the cleanest signal from the aerial which helps to better preserve the signal-to-noise ratio. Masthead amps tend to be either single output or 4 output but there are some with 5- and with 6-outputs. A more common combination is to use a single output masthead amp that then feeds an indoor multi-way amp for the rest of the house.
Note: with digital signals too much signal amplification can be just as bad as not enough signal. Beware buying something too powerful. A decent installer will (or should) carry a range of products and be able to test both signal quantity and quality at various points in the chain. That's part of the reason why we don't work for beer money; we are bringing a mobile TV and satellite shop to your home so we can tailor the system to overcome on-site issues. In this way we provide enough signal level compensation while maintaining signal quality without over-driving the TV's aerial inputs.