You can try keeping cells at 4 degree C. May be that will atleast slow down phagocytosis a lot

There are a number of inhibitors that will block endocytosis/phagocytosis via different mechanisms. Depending on how your particles are being engulfed, you'll have different sensitivities to these methods. From a quick literature search, some examples include: methyl-beta-cyclodextrin, phenothiazines, monodansylcadavrine, chloroquine, monensin, hyperosmotic sucrose, and Dynasore. I've used chloroquine before; it has a number of other effects on lysosomal pH and wouldn't be my first choice to block endocytosis. A friend used Dynasore to block endocytosis and seemed happy with the results. Keeping the cells at 4 degrees will definitely reduce phagocytosis but it can still occur at a slow rate and may not be helpful for whatever your next step is. 

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The point is, not to change the acidic milieu. In this respect, you should try all of the well known blockers of phagocytosis as indicated by Won Yong Lee and Nicole Messmer.

With kind regards

Josef Neumüller

Sodium azide may be a good choice, but it is highly poisonous and can also explode when it contacts metals like copper or lead as found in plumbing drains (if poured down drain).  Read all precautions before handling azide.  Make a 2% stock solution in water (about 0.3 M) in a fume hood and store in a capped glass container.  Dilute by 100 to 1000 in final working solutions, about 0.3 to 3mM final conc.  This is sufficient to kill microbes, will certainly stop phagocytosis and will kill cultured cells, too.  Azide will not fix cells like chemical fixatives, so with time (an hour or more) cells will form membrane blebs and will eventually lyse.

Alternatively, we have used 2% buffered PF for 10 to 30 min followed by buffer washing and storage at 4C with success.  However, fixing in 4% PFA or storing cells in PFA for hours or days will degrade fluorescence.  

An easy and cheap way to stop phagocytosis is incubating the cells with phrodo on ice. Often, in 4 degrees Celsius the cell stop the phagocytosis. Another way is using some drugs such as cytocalasin D, that inhibit polimerization of actin filament.

Good Luck

As suggested by Leandro Breda, I recommend to pour reaction mixture on ice.  Cells can be collected by centrifugation later.

In our laboratory, after incubation for 30 min, extracellular bacteria are removed by washing 3 times with PBS, following gentamycin (100 ug/ml) treatment to kill loosely adhere bacteria. followed by washing and analysis.

Best regards

Sagar