Yes, a proportional tax is more fair than a progressive tax. A proportional tax is also more easily administered, and would cost the government less, because there would not need to be so many agents to make sure that the tax is fairly collected. A progress tax discourages people from earning more money.
The proportional system of taxation was advocated by classical economists. Under this system, the individuals are required to pay tax in proportion to their income, the rate of tax remains same as the base changes. So proportional tax is better than progressive tax any day because you know what your tax will be.
In it's essence, although proportional tax at a glance would appear fairer one needs to considor the impact on lower earners. What about students looking to support themselves through education? Or young college students with no family? Semi retired individuals? Poorer familes with a low household income?
All of these individuals would lose the £10,600 tax free allowance making it significantly harder for costs to be met. With an equilibrium having been reached in the market assuming each person earning less than £100,000 pounds will receive (with the current lowest rate of tax) around £2,000 worse off.
If the tax became proportional though, the tax rate would need to increase significantly to account for the huge drop in revenues. This, coupled with the lack of a tax free allowance would cripple many lower income households and remove many of the incentives for young peolpe to get part times jobs whilst studying.