"begun to request" is a correct and usable structure in written English.
You can use this expression whenever you need to indicate that someone has started a process of asking for something. For example: After months of preparation, the government had finally begun to request the help of foreign aid organizations.
In December 1964, prisoners began to request to play soccer outside on a proper field.
In the late 1980s, he began to request books from the law library, looking for a way to overturn the conviction.
In December last year, the DEA finally began to request this information, setting a deadline for compliance of 1 February.
He understands the need for auditing and was happy to submit to the process, until line managers began to request that his reports were rewritten.
When African customers began to request that their goats be singed and Caribbean immigrants wanted their chickens roasted, a propane-powered blowtorch was promptly purchased.
FEMA, with the authorization of President Obama, had as of Monday afternoon declared a disaster in eight states and the District of Columbia, allowing them to begin to request assistance, before the worst of the storm hit.
As the boy grew older he began to request more, and in an act of self-sacrifice, the tree allowed the boy to cut her down and use the wood to build a boat and sail away.
"The change occurred because people who joined clubs in the '80s began to request classes that were less demanding on the backs, knees and ankles than traditional aerobics classes.
Frantic Galveston officials opened a shelter at a high school as more and more residents began to request help, Steve LeBlanc, the city manager, said in a televised interview late in the afternoon.
At the same time, the airlines say they expect an even greater demand for services geared toward passengers with limited mobility as more graying baby boomers begin to request wheelchairs at airports.
