Yes it can, and you can do it in one of two ways. Firstly, you could tax the vehicle online or by telephone; or you can do so at a post office. Both methods have advantages and disadvantages.
The advantage of taxing it by phone or online is convenience; you just go to the DVLA site via this link, fill in your details and you should be able to tax it with no problem provided that the MID database holds the details of your policy. The disadvantage is that it can sometimes take a while for the database to provide these details to the DVLA; the data is always sent by the insurer within 48 hours at the very most but that doesn't necessarily mean that the database itself is 100% efficient so sometimes, if the system cannot find your policy, you will just have to go down to your local general post office, or wait a day or two and try again.
In the vast majority of cases you will have no problem using your downloaded documents at the post office, not least of all because these have now been deemed officially acceptable by the DVLA. However, to make things a little more complex faxes and photocopies of documents are not acceptable; and there are still the odd few post office staff who do not like to be as cooperative as perhaps they should be, and they may still prove difficult if the printing is of poor quality, or if they have some other reason (reasonable or otherwise) to suspect that the documents may not be genuine. To get round this, it is possible, whilst filling in the proposal form, to tick a box and order a proper, hologrammed insurance certificate to be posted to you, which costs a small extra fee and which will be sent out, usually, by the next first-class post.
The upshot of all this is that if you wish to use short term car insurance to tax a car, you need to allow several days for either the MID database to update, or for your hologrammed insurance certificate to arrive, just in case you meet an awkward (expletive deleted) at the post office counter.
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