Based on what you say in the question, it is very likely that your children are automatically British citizens from birth. (The UK government may not know about them yet, but when they find out, the outcome will not be that the child becomes a British citizen as a result of the investigation, but that the government takes note of the fact that they've been a citizen all along!)
As such, the right way for them to enter the UK is not to get a visa, but one of
According to Wikipedia, the certificate of entitlement is much more expensive than the fee for an actual British passport, so your best bet would be to get your children British passports. If you do go for a certificate of entitlement, the standard electronic visa application is most certainly not how to apply for one; contact the British High Commission in Colombo for advice on what to do.
How about Sri Lankan authorities, then? Sri Lanka is not in general friendly towards dual citizenship, but it does seem to recognize that some people acquire more than one citizenship at birth. Section 20(2) of the Citizenship Act 1948 states that such a person loses Sri Lankan citizenship on their 22nd birthday, unless they explicitly renounce their other citizenship before then. Conversely, one infers that having dual citizenship up until the age of 22 must be allowed by Sri Lankan law.
Note that since British citizenship by birth occurs automatically, it will not necessarily shield the children from section 20(2) to ignore the fact that they're British citizens, such as by refraining from applying for a British passport for them. No matter whether they use their British citizenship, they would still have it, and still be obliged to make an explicit choice somewhen between their 18th and 22th birthday.
So no matter what you do now, you should make a note to investigate the relevant law regarding your children's nationality once they turn 18, so they won't lose citizenship by inaction.