Lawn Weeds

Not in anyway green fingered so looking for some help/advice. Large lawn filled site in a boggy area. Always had drainage issues. About 2 yrs ago redid lawn when doing some building work. Brought in a lot more earth and did a pretty decent job. Decided at time not to instill expensive drainage,,,,,subsequently dug a channel myself which works quite well. Ground still gets wet but when we get couple dry days together firms up pretty well. My problem is with soft weeds. Quite a lot of the lawn has these weeds and as a result grass growth poor in these areas. (I think topsoil used by guy who did lawn quite poor).
He told me that with constant mowing they would gradually disappear but not so. Am reluctant to spray with weed killer for grass sake but if that is what it takes so be it. Should i just spray kill the areas...scarify spread new earth and go again?......From research i thought these could be lawn ivy but dont think so looking at pics......more akin to 3leaf clover tho no flowers appear...
Then again aside from aesthetics.....as in i would love a perfect green lawn.....i know living in rural area going to get weeds/flowers etc from surrounds. Also for now main purpose of area is kids football/hurling general destruction.....Its green and soft....should i just leave alone...it serves its function....just doesnt look like i would like it to!
Thanks all

Hi - most lawn weeds would be controlled / killed off when you spread something like "evergreen" - look for the moss / weed killer on the labels. Just don't over use as it will scorch the grass...
Regular mowing (make sure the lawnmower blade is sharp)will keep the lawn healthy & will allow the grass to smother out the weeds. When mowing, make sure the grass is dry & never take more than one third of the grass length off in any one mowing.... it's hard to keep a lawn looking good all the time, especially with kids / pets on it... all depends on the look you want against the function that you need the lawn / grass area for...

You can get some lawn sand & some bagged top soil for the "poor areas" to help the grass... make sure to aerate the area & for any bald areas, throw some grass seed on it, rake it in (you can do this from April on)... just don't use the fertliser at the same time of / or after the grass seed is put down...

Another thing I found is defining the border of the grass area to highlight it... make sure grass edge is defined, clean angles for the eye, contrast colours on border areas with flowers / plants... helps define the grass area more... Hopefully we'll get a good summer that can be spent outdoors enjoying the garden!