Traveling to UK on visit visa as a Syrian citizen?

When you arrive in the UK, you will speak with an Immigration Officer and at that time you can ask him/her to vary your 'end date'. They can if they want, but do not have to do it and most of the time they not do it.

This is addressed in Paragraph 31A of the Immigration Rules, which states...

Where a person has arrived in the United Kingdom with leave to enter or remain in the United Kingdom which is in force but was given to him before his arrival, he may apply, on arrival at the port of entry in the United Kingdom, for variation of that leave. An Immigration Officer acting on behalf of the Secretary of State may vary the leave at the port of entry but is not obliged to consider an application for variation made at the port of entry. If an Immigration Officer acting on behalf of the Secretary of State has declined to consider an application for variation of leave at a port of entry but the leave has not been cancelled under paragraph 2A(8) of Schedule 2 to the Immigration Act 1971, the person seeking variation should apply to the Home Office under paragraph 32.

Source: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/420595/Immigration_rules_part_1_master_20150406_v1_final.pdf

...or in plain English: You can try to get a variation, but they do not have to grant it if they do not want to. If they agree, they will know what to do and what to put in your passport. If they refuse, your original 'end date' must be observed.

A refusal at port to vary leave does not create a pejorative immigration history. But a port side cancellation of leave does.

Needless to say, your request should be well supported by documents along with a reasonable explanation. Outcomes may also be heavily influenced by personal impact and articulation skills, but once they say they will not do it, the best advice is to let it go.

Adding...

The Home Secretary issued a Ministerial Authorisation affecting Syrian nationals on 27 Feb 2015 and this is still in force. You may be able to benefit from it. Or may not.

I have agreed a ministerial authorisation (Equality (Syria—Entry clearance outside the immigration rules) Authorisation 2014) to allow differentiation in favour of Syrian nationals whom we want to bring to the UK under the VPR scheme.

Plus a new rule for Syrians came in to effect in March 2015...

A Statement of Changes to the Immigration Rules HC 1116 was published on 16 March 2015. These changes specifically affect Syrian nationals who are travelling through the UK on certain types of visit visas for entry to United States of America.

More info at Immigration Law Practitioners Association