Hi Dhyeya,
After consulting a few Immigration Experts, I got was a mixed response to my situation. In fact some Immigration Specialist advised me not to travel, while others advised me tectonically and legally if my Visa Expires on the 14; I'm legally entitled to travel on the 12th and get back on the 13th without any issues.
The reason for the misinformation is the so called Immigration Specialist want to make 350 just trying to scare you and advise you of the worst case scenarios.
After giving a call to the UK Visas & Immigration Phone line, the first lady who answered me advised that legally I have no issue on traveling and getting back, but the final decision lies on the 'Entry Clearance Officer'. Not satisfied with the answer, I called back again on the next day and a nice gentleman from the UKVI advised me that there should be no issues, but to be on the safe side take copies of my appointment and payment slips of the PEO appointment. And further to this I was also advised to carry a official letter from the company stating the purpose of my Business Travel and return dates.
If you are traveling genuinely for business and having been doing so as my self, I don't think you should have any issues, unless you have some ambiguous issue in regards to your travel.
Furher to this, I did send a email to the PEO office and got the following responce from the UKVI:
Dear Sir / Madam
Thank you for your email of 6th May 2014.
Border Force staff based at ports of entry, decide whether to grant entry to a person arriving into the United Kingdom through the immigration control at the time of arrival, on a case by case basis. We cannot advise on a case in advance of that arrival.
As it is your intention to apply for ILR, it is advisable you take your email confirming your Premium Service Centre appointment. As well as this you could carry evidence to show you live and work in the UK. The number of days remaining on your visa is not as significant as your intentions and a foreign national will be required to show a valid visa allowing them entry to the UK, for those categories where this is required, along with evidence that they are entering or re-entering for the same purpose.
I hope that this is of some assistance to you.
Yours faithfully
F-- M-----
UK Visas & Immigration
Finally I decided to travel on the 11th and get back on the 14th (i.e. still having 30 days on my Visa). I did take the Appointment Letters, payment Slips, as well a Reference Letter from my work. Upon arrival the entry clearance office only asked me for how long I have been out and processed my entry in less than 2-5 minutes.
I hope the above clarifies the situation and help you in some way. This could be different from case to case, and this is not a definite answer on the issue, I would still advise you to contact the UKVI and ask their advise on your case.
Best regards,
FT