Disclaimer: I am not a tax adviser or accountant, just someone who has done a tax return (for a partnership) for several years and is also employed...
As far as expenses are concerned, the situation depends in part whether you are employed or self-employed.
If you are employed, common practice would be that your employer pays your travel expenses and often they will get a dispensation from HMCE that you don't need to declare expense payments from your employer on your tax return (if the expenses were restricted by the employer to HMCE-approved rates/types of claim, the columns for payments and expenses on your tax return would balance out anyway).
There's a fairly clear rule that travel to and from your normal place of work is not usually an allowable expense (your employer can choose to pay it, but it is a taxable benefit if they do). The exception is where you are normally a public transport user and are exceptionally required to work when no public transport is suitable.
If you are self-employed then travel to customer sites is generally an allowable expense (but bear in mind there are strict rules defining what is self-employment vs employment which may apply if you always work in one place for one customer).
To answer your overall question: Most people who have a single continuing employment only will not be likely to see a refund of any substance from doing a tax return (you still have to do one if asked, though!). PAYE gets things close enough for many people. If you are self-employed, rent out property etc. it will become much more significant. This is not a complete list of circumstances and if you're unsure then you should contact a tax office or an accountant, obviously. Maybe if you say a little more about whether you are employed or not it would clarify - which pages are you filling out?