Can I enter the UK on a visitor visa if I broke up with my sponsor (girlfriend)?

A Standard Visitor Visa works any time between the start and end dates (all other things being equal). A break down in the relationship between the visitor and the sponsor (especially when the the relationship is romantic) happens regularly.

Can I still use the visa to enter if I'm not in direct communication with my sponsor?

The answer is yes, but heavily qualified. Since the relationship was a material factor in granting your entry clearance, you have a classic "change of circumstances"; material change of circumstances must be reported during the landing interview. If they are not reported you become an illegal entrant under Part 9 of the Immigration Rules. This should be avoided because it can be discovered at any point in the future and having a record as an illegal entrant can lead to embarrassment and other unsavoury circumstances.

If you conceal it because the IO doesn't bring it up, they can get you later for deception by silence (Immigration and Asylum Act 1999) Hence it's time well spent to think up how you are going to declare it.

I assume you are still committed to your girlfriend and a part of your visit will be devoted to sorting things out, so your statement to the Immigration Officer would go something like this...

I have a material change of circumstances to report. (IO says 'What is it?') I have been sponsored by my girlfriend and the relationship has broken down. (IO says 'Is it a temporary breakdown?'). I am attempting to repair the relationship but I cannot guarantee success, during this visit my accommodation and maintenance are blah blah blah. (IO says 'May I see your reservations and bookings for your visit along with your itinerary?'). My itinerary is blah blab blah...

If you are not committed to fixing the relationship, you will have to use a different declaration. This would go along the lines of...

I have a material change in circumstances to report. (IO says 'What is it?'). I had a girlfriend sponsor my application, but the relationship has irrevocably broken down and I will not be visiting her on this occasion. Accordingly I have made alternative maintenance and accommodation arrangements. (IO says 'May I see those arrangements?' and 'What is the purpose of your visit?'). I am here for 'x' days to blah blah blah... (IO says 'May I see your recent bank statements and other evidence?'). Of course, I have the evidence submitted originally along with updates that are more recent, blah blah blah, yada, yada, yada...

Optionally, if you are comfortable on discussing technicalities with an IO, you can add...

Although this is a change of circumstances, it has been adequately declared along with a reasonable premise for my visit and would not fall to be reckoned with under Paragraphs 320/321 of the rules. This is because blah blah blah blah...

In both cases things seem to work better if you spill it out before they start asking questions. If you wait for it to come up as part of the IO's enquiry, he can think 'Aha! Gotcha!'. So don't let that happen.

There are also situations where the sponsor becomes hostile and vindictive. This can manifest in notifying UKVI about your arrival or your whereabouts; this does not result in an automatic removal from port because there are no binding constraints between a visitor and a sponsor like there are between a spouse and a sponsor. And from a practical viewpoint they don't have the time or resources to deal with every vindictive girlfriend/boyfriend anyway (it happens a lot)

So if you have an explanation for each of the various possibilities above, you should have no problems (all other things being equal).

If yes, what documents might be required at Immigration?

Bring everything you submitted during the application stage along with high quality evidence of your new maintenance and accommodation. You should have high quality evidence of how you will support yourself during your stay.

It is also critical to have something to support the variance in your premise; if you do not have a legitimate premise that you can support, expect problems. In other words if you are coming to the UK to 'hang out' or 'visit friends', they will be worried that your intent is too vague.

See also Should I submit bank statements when applying for a UK Visa? What do they say about me?

See also Schengen Visa Refusal: Justification for the purpose and conditions of the intended stay was not reliable Although it is about Schengen visas, a lot of it is applicable to your case.

Note

• People reading this answer should take note that the same is not true for T2's, T2 (ICT), some T5's, and anyone on the family formation track. Those types of visas require an active sponsor for the duration and the visa becomes invalid at the point when the relationship no longer exists.

• As always, for ANYBODY entering the UK as a visitor, it is best practices to have all your evidence and supporting materials neatly organised in A4 pockets (or equivalent) in an A4 ring binder (or equivalent). The sections would be: invitations followed by premise support followed by financial capacity, then maintenance and accommodation, then performance history, and finally print-outs from Google Maps with pin drops on the itinerary locations. This is best practices only and certainly not a requirement. Your mileage may vary.

As per @ GayotFow's request, I am posting this comment as an aswer.

Are you certain that you want to risk not being admitted and having future applications turned down?

If you don't tell about the breakup and they somehow find out (unlikely, though it is), that will probably happen. But, if you do tell them ...

If I were you, I think that I would apply for a new visa.

UK policy allows only one visa at a time. If the previous visa has not expired it will cancelled without prejudice when the new one is issued.

Also note that with a Standard Visitor Visa any combination of business/pleasure/tourist/conference/relationships is allowed. There is no required order or fixed proportion for any of the permitted activities.

Permitted activities are listed in Appendix V of the Rules.