Dfyjkt

On 25th of November 2015, I was granted a 6 months C-VISIT visa for UK.
I entered the country on 22nd of March 2016 and my visa expires on 25th of April.
On my entry application I noted that I will stay for 30 days.
Am I eligible to extend my visa?

Based on this information: gov.uk/standard-visitor-visa/extend-your-visa, I should be eligible to extend my visa. I've called UK Visas and Immigration centre and I was said that C-VISIT visa cannot be extended. The lady on the phone was very surprised when I've told her that I have another information from their website and told me that I could try.

I'm confused now: can I extend my visa or not?

Actually, I was calling them for another question.
This application: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/516833/FLR_O__Version_04-16.pdf requires my Biometric residence permit in the Section 4:

Note 1 In accordance with regulation 3 of the Immigration (Biometric Registration) (Amendment) Regulations 2012 anyone applying for an extension of stay in the UK in the categories for which this application form is specified must also apply for a biometric immigration document, otherwise known as a biometric residence permit.

But you can't have one if you're a visitor. In the meantime, they are referring this link: https://www.gov.uk/biometric-residence-permits that says:

You don’t have to apply for a BRP. You’ll get one automatically as part of your visa or immigration application.

When you make your visa or immigration application you have to give the personal data that appears on your BRP.

I am really confused now. Can somebody help me with this?
Can I extend my visa or not? Do I need a BPR?

There are no provisions in the rules for extending a Standard Visitor Visa (the UK type "C") except as below...

• The visa was issued for a period less than 6 months and you want to
  extend to a full 6 months;

If you qualify, you can fill out an FLR(O) form and take it to the Home Office along with the £1,622 fee (yes you read it right, one thousand six hundred twenty-two pounds). They will keep the fee even if the application is refused. The main downside to FLR(O) is that they may revoke your visitor visa on "change of circumstances". They are entitled to do that and if they opt to do it you will be detained and removed.

Otherwise the visa expiry date is the last day which you can lawfully remain. It doesn't matter if the visa was issued for 6 months and you only used 1 month, the expiry date is a fixed and immutable point and does not 'float' according to the person's arrival date.

To extend beyond 6 months is not possible and you should submit a new application from your home country. Nothing prevents you from trying however. You can use one of the FLR applications, presumably FLR(O). The downside is that applications made by a visitor are non-suspensive so you become an overstayer on the visa expiry date or the decision date (if your existing leave is revoked) whichever is earlier.

For your other question, about getting a Biometric Residence Permit, you do not qualify for one because your visa was issued for a period less than (or equal to) 6 months.

From https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/490874/Visitor_guidance_v4_0.pdf:

Extensions for long-term and multiple-entry visit visas If a visitor holds a long-term multiple-entry visa and they want to stay
for longer than the visa expiry date, it is possible for them to apply
to extend their leave for up to the maximum 6 months permitted for
visitors (standard). For example a visitor arrives in January and
their long-term visit visa is due to expire in February. Provided the
visitor meets the rules, they can extend for up to 6 months, until
June, as a visitor (standard). A single entry or 6 month visa can also
be extended to complete 6 months’ in the UK as a visitor.

This is aplicable if you have a long-term visa (2, 5 or 10 years), which is not the case here. I'll just leave it here as an information for others.